Sets, Relations and Functions — practice questions

243 curated practice questions from Sets, Relations and Functions (Mathematics JEE Main, NTA Exams) — 72 medium, 24 hard, 147 easy. Every question includes the final answer free; step-by-step worked solutions with a free account.

• If the domain of the function f ( x ) = cos –1 ( 2-|x| 4 )+ _ e (3-x) ^ -1 is [–a, b) – γ , then + + is equal to
• The minimum value of f(x)=e^ x^ 4 -x^ 3 +x^ 2 is
• ^ -1 ( )- ^ -1 ( )= x , then sin x is equal to
• A function f from the set of natural numbers to integers defined by f(n)= array ll n-1 2 , & when n is odd - n 2 , &…
• If 1, 2 = 1, 2, 3, 5, 9 , then
• Find the domain of definition of the function f(x)= _ 4 [ _ 5 [ _ 3 (18 x-x^ 2 -77 ) ] )
• The number of solutions of the equation ^ -1 ( 1+x^ 2 2 x )- ^ -1 x= 2 + ^ -1 x is given by
• If = ^ -1 ( 3 5 ) , = an ^ -1 ( 1 3 ) , where , then α – β is equal to
• If A= x R:|x|<2 and B= x R:|x-2| 3 then :
• If x 2 – 1 2 – x – 2 > 0, then x lies in the interval set
• If the inverse trigonometric functions take principal values, then ^ -1 ( 3 10 ( ^ -1 ( 4 3 ) )+ 2 5 ( ^ -1 ( 4 3 ) ) )…
• ^ -1 ( 2 3 )+ ^ -1 ( 7 6 )+ ^ -1 ( 3 4 ) is equal to :
• All x satisfying the inequality (cot –1 x ) 2 – 7(cot –1 x ) + 10 > 0, lie in the interval
• Indicate the correct alternative : The number l og 2 7 is
• Let f be a function satisfying f(x+y)=f(x) f(y) for all x, y R . If f(1)=3 , then _ r=1 ^ f(r) is equal to
• Range of the function f (x) = x^ 2 +x+2 x^ 2 +x+1 ; x ∈ R is
• Let f(x)=2^ -(x) and g(x)= array c -1 if x>0 0 if x=0 1 if x where (x) is fractional part of x . Then for all x …
• The set of values of x satisfying the inequalities (x – 1) (x – 2) 0 is
• Let f : R → R be defined by f(x)= |x|-1 |x|+1 then f is:
• If f(x+y, x-y)=x y . then the arithmetic mean of f(x, y) and f(y, x) is
• If f : R → S, define by f (x) = sin x – cos x + 1, is onto, then the interval of S is
• If cos –1 x – cos –1 y 2 = , then 4x 2 – 4xy cos α + y 2 is equal to
• If a function f : [2, ∞) → B defined by f (x) = x 2 – 4x + 5 is a bijection, then B is :
• Let Z be the set of integers. If A= x Z: 2^ .(x+2) x^ 2 -5 x+6 ) =1 and = x Z:-3<2 x-1<9 , then the number of subsets…
• Let the domains of the functions f ( x ) = log 4 log 3 log 7 (8 – log 2 ( x 2 + 4 x + 5)) and g(x)= ^ -1 ( 7 x+10 x-2 )…
• The domain of the function f(x)= ^ -1 ( 1-|x| 2 ) is
• Range of the function f( x )= x 1+ x ^ 2 is
• If a f (x + 1) + b f ( 1 x+1 )=x, x ≠ −1, a ≠ –b, then f (1) is equal to
• Let f : [–1, ∞) → R be given by f (x) = (x + 1) 2 –1, x > –1 . Then f –1 (x), is :
• The set of values of x which satisfy the inequations 5x + 2 < 3x + 8 and x+2 x-1 <4 is
• Find the domain of the function f(x)= 1 [x]^ 2 -7[x]+10 , where [.] denotes the greatest integer function
• Find the domain of the function f(x)= _ 2 (x+3) x^ 2 +3 x+2
• For x R- 0,1 , let f_ 1 (x)= 1 x , f_ 2 (x)=1-x and f_ 3 ( x )= 1 1- x be three given functions. If a function, J(x)…
• If f(x)= [a-x^ n ]^ 1 / n , where a>0 and n is a positive integer, then f^ f [f( x )] is equal to:
• Let f be a function from R to R given by f (x) = 2x + |cos x|. Then f is
• Let N be the set of natural numbers and a relation R on N be defined by R= (x, y) N N: x^ 3 -3 x^ 2 y-x y^ 2 +3 y^ 3 =0…
• A real valued function f(x) satisfies the functional equation f(x-y)=f(x) f(y)-f(a-x) f(a+y) where ' a ' is a given…
• If cos –1 x – cos –1 = α, where –1 ≤ x ≤ 1, –2 ≤ y ≤ 2, x ≤ then for all x , y , 4 x 2 – 4 xy cosα + y 2 is equal to
• The inverse of the function f(x)= a^ x -a^ -x a^ x +a^ -x is (where codomain of f(x) is (–1, 1))
• The domain of the function f (x) = l og e (x – [x]), where [.] denotes the greatest integer function, is
• Let W denotes the words in the English dictionary. Define the relation R by R = (x, y) ∈ W × W : the words x and y have…
• The function f : R → R defined by f (x) = (x – 1) (x – 2) (x – 3) is
• If [x] 2 = [x + 2], where [x] = the greatest integer less than or equal to x, then x must be such that
• Let A = x : x is a multiple of 3 and B = x : x is a multiple of 5 . Then is given by
• The equation 2 ^ -1 x+ ^ -1 x= 11 6 has :
• f( x )= array l x , if x is rational 0, if x is irrational array . and g( x )= array l 0, if x is rational x , if x is…
• Considering only the principal values of inverse functions, the set A= x 0: ^ -1 (2 x)+ ^ -1 (3 x)= 4
• The equation 2 sin 2 x 2 . cos 2 x = x + 1 x , 0 < x < 2 has
• Set of values of x satisfying cos –1 x > sin –1 x
• Find the period of f(x)= x+ x z + x z^ 2 + x z^ 3 + + x z^ n-1 + x z^ n
• Let f(x) defined on [ -2, 2] and is given by f(x)= array ll -1, & -2 x 0 x-1, & 0 x 2 array and g( x )=f| x |+|f( x )|…
• The range of the function y = l og 3 (5 + 4x – x 2 ) is
• Let f(x)=x^ 2 , x R . For any A R, define g(A) = x R : f(x) A . If S = [0, 4], then which one of the following…
• If A = x : x = 3 n , n ≤ 6, n ∈ N B = x : x = 9 n , n ≤ 4, n ∈ N then which of the following is false ?
• The domain of the function is
• [ ( x _ 1 - x _ 2 ]^ 2 + [12+ 1- x _ 1 ^ 2 - 4 x _ 2 ]^ 2 ] x _ 1 , x _ 2 R is
• If α = tan –1 ( 5 4 ) and β = tan –1 (- 2 3 ), then
• If y=1+ x 1! + x ^ 2 2! + x ^ 3 3! + , then the value of d y d x is
• The domain of the function f ( x ) = sin –1 ( x^ 2 -3 x+2 x^ 2 +2 x+7 ) is:
• The domain of the function f (x) = log 2 (log 3 (log 4 x)) is
• f(x) = x( x+ x) [ x+ ]- 1 2 , where [∙] is greatest integer function, is
• If a > b > 0, then the value of ^ -1 ( a b )+ ^ -1 ( a+b a-b ) depends on
• Let R be the set of real numbers. If f: R R is a function defined by f(x)=x^ 2 , then f is
• A function f : A → B, where A = x :-1 x 1 and B = y: 1 y z is defined by y=f(x)=1+x^ 2 Which of the following…
• If the function y= (f(x)) is monotonic for all values of x (where f(x) is continuous), then the difference between the…
• If R is a relation from a finite set having m elements to a finite set B having n elements, then the number of relation…
• The value of (2 ^ -1 ( 3 5 )+ ^ -1 ( 5 13 ) ) is equal to
• f: (0, 2 ) A_ 1 f(x)= _ 2 ( x^ x +1 ) , then the minimum value of f(x) is
• Let f : R → R be a function given by f (x + y) = f (x) + f (y) for all x, y ∈ R such that f (1) = a. Then, f (x) =
• The largest interval lying in ( - 2 , 2 ) for which the function, f(x)=4^ -x^ 2 + ^ -1 ( x 2 -1 )+ ( x) is defined, is
• The domain of f (x) = _ 2 (x+3) x^ 2 +3 x+2 is
• If 2 tan –1 (cos x) = tan –1 (2 cosec x), then the value of x is :
• If f(g(x)) = | cos x |, g(f(x)) = cos 2 x , then -
• If the domain of the function f(x)= ^ -1 x^ 2 -x+1 ^ -1 ( 2 x-1 2 ) is the interval (α, β], then α + β is equal to
• Find the no. of solutions of |[x]-2 x|=4 , where [ x ] is the greatest integer x
• The number of real solutions of [e^ x ]=5^ x +5^ - x is
• If f: 1,2,3, 0, 1, 2, is defined by f(x) = array r x 2 , if x is even - x -1 2 , if x is odd array . then the value of…
• Find the range of the function f(x)= x 1+x^ 2
• The domain of the function f(x)= ^ -1 (3-x) (|x|-2)
• Number of solutions of the equation ^ -1 ( 1 2 x +1 )+ ^ -1 ( 1 4 x +1 )= ^ -1 ( 2 x ^ 2 ) is
• Let f (x) = cos 3x + sin 3 x . Then f (x) is
• Let A = 2, 3, 4 and X = 0, 1, 2, 3, 4 , then which of the following statements is correct
• Consider the functions f(x)= x and g(x) = 7x + b. If the function y = fog(x) passes through (4, 6) then the value of b…
• If the function f:[1, ) [1, ) is defined by f(x)=2^ x x-1 , then f^ -1 (x) is
• Let f(x)=2^ 14 x+1 and g(x)=3^ 11 x-1 . If (f a g)(x)=x , then x is equal to:
• If ^ -1 ( x 5 )+ cosec ^ -1 ( 5 4 )= 2 , then the value of x is
• Let f(x) be a function given by f(x)= x^ 2 +1 [x] for all x ∈ [1, 4), where [.] denotes the greatest integer function…
• Considering only the principal values of inverse trigonometric functions, the number of positive real values of x…
• If f (x) = x 2 – 3x + 1 and f (2α) = 2 f (α), then α is equal to
• The value of ^ -1 3 4 + ^ -1 5 13 is :
• If the domain of the function f ( x ) = log e (4 x 2 + 11 x + 6) + sin –1 (4 x + 3) + cos –1 is (α, β], then 36 |α + β|…
• Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of…
• If a function f(x) satisfies the condition f (x+ 1 x )=x^ 2 + 1 x^ 2 ,(x 0) , then f(x) equals
• The largest interval among the following for which x 12 – x 9 + x 4 – x + 1 > 0 is
• Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which…
• The domain of definition of function f(x)=6 4^ x +8^ (2 / 3)|x-2| -52-2^ 2(x-1) is
• Considering the principal values of the inverse trigonometric functions, ^ -1 ( 3 2 x+ 1 2 1-x^ 2 ), - 1 2 <x< 1 2 , is…
• A survey shows that 63% of Americans like cheese whereas 76% like apples. If x % of Americans like both cheese and…
• Find the domain for function f(x)=[ x] ( [x-1] )
• Let f : R → R be a function such that f (x) = x 3 – 6x 2 + 11x – 6 . Then
• Let f(x)=n x+n-[n x+n]+ x 2 , where [ x ] is the greatest integer ≤ x and nE N. It is
• If ^ -1 ( x )- ^ -1 ( x )= x , then x equals :
• If f ( x )= 2- x and g(x)= 1-2 x , then the domain of f [g (x)] is
• The inverse of the function y = [1 – (x – 3) 4 ] 1/7 is
• If θ = sin –1 x + cos –1 x – tan –1 x, x ≥ 0, then the smallest interval in which θ lies, is given by :
• Let A, B and C be sets such that A B C . Then which of the following statements is not true?
• If a = sin –1 (sin (5)) and b = cos –1 (cos(5)), then a 2 + b 2 is equal to
• Determine the value of x satisfying the equality | (x^ 2 +4 x+9 )+(2 x-3) |= |x^ 2 +4 x+9 |+|2 x-3| .
• Let _ k=1 ^ 10 f(a+k)=16 (z^ 1 a -1 ) , where the function f satisfies f(x+y)=f(x) f(y) for all natural numbers x, y…
• Let A = x : x is a digit in the number 3591 , B = x : x ∈ N, x < 10 . Then, which of the following is false ?
• The inverse of the function y= [1-(x-3)^ 4 ]^ 1 / 7 is (Assume that y is bijective)
• If f(x) = sin 2 x, g(x)= x and h(x) = cos –1 x, 0 ≤ x ≤ 1, then -
• The domain of the function, f(x)= 4-x^ 2 ^ -1 (2-x) is
• Find the set of values of ‘x’ for which the given condition is true (x – 1) (x – 3) (x + 5) > 0
• If ( ^ -1 x )^ 2 - ( ^ -1 x )^ 2 =a ; 0 x a ≠ 0, then the value of 2 x 2 – 1 is
• The range of k for which ||x–1|–5| = k have four distinct solutions -
• If x = sin –1 (sin10) and y = cos –1 (cos10), then y – x is equal to
• If f(x) and g(x) are two functions with g(x) = x- 1 x and f g(x)=x^ 3 - 1 x^ 3 , then f^ ( x ) is :
• If ^ -1 x-1 x+2 + ^ -1 x+1 x+2 = 4 , then x is equal to :
• For a > 0, solve the equation for x: 2 _ x a+ _ a x a+3 _ a^ 2 x a=0
• Find the domain of f(x)= cosec x +( x)^ 1 / 3 .
• A function f : A → B, where A x : – 1 ≤ x ≤ 1 and B = y : 1 ≤ y ≤ 2 is defined by the rule y = f (x) = 1 + x 2 . Which…
• The domain of sin –1 [ _ 3 ( x 3 ) ] is
• If the domain of the function is (a, b], then the value of is equal to
• The inverse of the function f(x)= 10^ x -10^ -x 10^ x +10^ -x is (Assume that f(x) is bijective)
• If f(x)= x x-1 , [fo fo fo ..... of) (x) composition functions taken odd number of time, is equal to:
• If f(x)= 9^ x 9^ x +3 , then find the value of f ( 1 1996 )+f ( 2 1996 )+f ( 3 1996 )+ +f ( 1995 1996 )
• If A and B are any two sets, then is equal to
• If c 2 + (c + d) x + cd < 0, then x belongs to.
• Let x * y = x 2 + y 3 and ( x * 1) * 1 = x * (1 * 1) Then a value of 2 ^ -1 ( x^ 4 +x^ 2 -2 x^ 4 +x^ 2 +2 ) is
• Let f( x )= x 1- x and let a be a real number. If x _ t = a _ 1 , x _ 1 =f ( x _ t ), x _ 2 =f ( x _ 1 ), , x _ 1 g g…
• The value of _ r=0 ^ ^ -1 ( 1 1+r+r^ 2 ) is equal to :
• The value of ^ -1 9+ cosec ^ -1 ( 41 4 ) is given by:
• cos –1 (cos(–5)) + sin –1 (sin(6)) – tan –1 (tan(12)) is equal to (The inverse trigonometric functions takes the…
• Find the range of the function f(x)= 2+x 2-x
• Let f (x) be a function defined on [0, 1] such that f(x)= array cc x & x Q 1-x, & x Q array . Then for all x ∈ [0, 1]…
• Let S be the set of all α R such that the equation, 2 x+ n x=2 x-7 has a solution. Then S is equal to:
• Let A = x R : x is not a positive integer . Define a function f : A → R as f(x)= 2 x x-1 , then f is:
• Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation…
• The function f(x) = ^ -1 x x-[x] is defined for all x belonging to
• The value of ( _ n=1 ^ 50 ^ -1 ( 1 1+n+n^ 2 ) ) is
• Given below are two statements. STATEMENT - 1: Let f be a differentiable function satisfying f(x+y)=f(x)+f(y)+7 x y-1…
• If ^ -1 x= 5 , for some x ∈ (–1, 1), then the value of cos –1 x is :
• The solution set of x^ 2 -3 x+4 x+1 >1, x R is
• Let f(x)= _ 2 ( x),(0<x< ) and g(x)= ^ -1 (e^ -2 ),(x 0) . If α is a positive real number such that a=(f g)^ (a) and…
• Range of f(x) = sin –1 x + tan –1 x + sec –1 x is
• a f(x+1)+b f ( 1 x+1 )=x_ i x -1_ i a b , then f (2) is equal to
• The function f (x) = cos ( (x+ x^ 2 +1 ) ) is :
• The real valued function f(x)= cosec ^ -1 x x-[x] where [ x ] denotes the greatest integer less than or equal to x , is…
• If f(x+y)=f(x)+f(y)-x y-1 for all x, y E and f(1)=1 , then the number of solutions of f(n)=n_ 1 n N is
• If tan(cos –1 x) = sin ( ^ -1 1 2 ) , then x is equal to :
• Find the domain of y= ^ -1 ( _ 2 x )
• If A = 1, 3, 5, 7, 9, 11, 13, 15, 17 , B = 2, 4, .......,18 and N is the universal set, then A c ((A B) B c ) is
• f (x) = x + x ^ 2 is a function from R → R. Then f (x) is
• The value of x for which x-3 4 -x 2 – x > 2x – 8
• The value of cos (2 cos –1 x + sin –1 x) at x = 1 5 is :
• A function whose graph is symmetrical about the y-axis is given by
• Let [ x ] denote the greatest integer less than or equal to x . Then the domain of f ( x ) = sec –1 (2[ x ] + 1) is :
• If ^ -1 1 1+2 + ^ -1 1 1+(2)(3) + ^ -1 1 1+(3)(4) + . .+ ^ -1 1 1+n(n+1) = ^ -1 , then θ =
• If 3 f (x) + 5 f ( 1 x )= 1 x -3, x(≠ 0) ∈ R, then f (x) is equal to :
• Given below are two statements. Consider the function f(x) satisfying the relation f(x+1)+f(x+7)=0 x R . Statement - 1…
• If domain for y=f(x) is [ - 3, 2 ]. Find domain of g( x )=f |[ x ]| ?
• The graph of the function y = f (x) is symmetrical about the line x = 2, then
• If f(x)= 2 x-1 x+5 (x -5) then f^ -1 (x) is equal to :
• The domain of the function f (x) = ^ -1 (x-3) 9-x^ 2 is
• The function f( x )= x -[ x ]+ x , where [ x ] = the greatest integer less than or equal to x , is a
• If 3 f(x)-f ( 1 x )= _ x x^ 4 , for x>0, find f (e^ x )
• If f(x)= x|x| 1+x^ 2 , then f^ -1 (x) equals
• Range of f (x) = sin –1 x + cot –1 x + tan –1 x is
• If f( x )= ( 1+ x 1- x ) then f ( 2 x 1+x^ 2 ) will be equal to:
• The domain of the function f(x)= ^ -1 ( |x|+5 x^ 2 +1 ) is (– ∞, – a ] ∪ [ a , ∞). Then a is equal to
• If the domain of the function sin –1 is (α, β], then 3α + 10β is equal to
• The domain of f(x) = (x^ 2 -1 )^ x ^ x
• Find the period of [ x +4 x +9 x + +n^ 2 x ] :
• The number of solutions of the equation ^ -1 [x^ 2 + 1 3 ]+ ^ -1 [x^ 2 - 2 3 ]=x^ 2 for x ∈ [–1, 1] and [ x ] denotes…
• If _ r=1 ^ 50 ^ -1 1 2 r^ 2 =p then the value of tan p is
• Let f(x) = x-[x] 1+x-[x] , x ∈ R, then the range of f is :
• Let f and g be increasing and decreasing functions respectively from [0, ) to [0, ) Let h(x)=f(g(x)) If h(0)=0, then h(…
• The period of f(x)= ( x -1 )+ ( x ) n ∈ 7 , n > 2 is:
• A function f , from the set of natural numbers to integers, defined by f(n) = array l n-1 2 , when n is odd - n 2 …
• The value of [ 3 4 ]+ [ 3 4 + 1 100 ]+ [ 3 4 + 2 100 ]+ + [ 3 4 + 99 100 ]=
• The sum of all real roots of the equation |x - 2| 2 + |x - 2| - 2 = 0 is
• Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A E , each…
• Find the range of the function f( x )= x + - x , where . denotes fractional part.
• Let f (x) = sin x and g (x) = In |x|. If the ranges of the composition functions fog and gof are R 1 and R 2…
• If 5(x)=x+[x] and [x]- x = 1 2 (where (x) and [ x ] are fractional and integral part of x ), then x is :
• The number of values of x , where the function f(x)= x+ ( 2 x) attains its maximum, is
• The domain of function y= _ 10 _ 10 _ 10 _ 10 (up to n terms) is
• Let f( x )= _ x ^ 2 25 and g(x) = l og x 5 then f (x) = g (x) holds for x belonging to
• Let f (x) = x^ 2 x+1 , x -1 . The value of α for which f (a ) = a, (a ≠ 0) is
• Let f(x)= x^ 2 -4 x^ 2 +4 , for |x| 2 then the function f:(- ,-2] [2, ) (-1,1) is:
• The number of real solutions of x- 1 x^ 2 -4 =2- 1 x^ 2 -4 , is / are
• If f(x)+2 f ( 1 x )=3 x, x 0, and 5= x R: f(x)=f(-x) , then S:
• The function f(x)= [ (x+ x^ 2 +1 ) ] is:
• If ^ -1 (x-1)+ ^ -1 x+ ^ -1 (x+1)= ^ -1 3 x , then x is
• If f(x+1)+f(x-1)=2 f(x) and f(0)=0 , then f(n) , त E N .
• Considering only the principal values of the inverse trigonometric functions, the domain of the function f(x)= ^ -1 (…
• For any two sets A and B if A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X, then
• Let f(x)=a^ x (a>0) be written as f(x)=f_ 1 (x)+f_ 2 (x) , where f_ 1 (x) is an even function and f_ 2 (x) is an odd…
• Let f: R R be a function such that f(x)=a x+3 x+4 x . Then, f(x) is invertible if
• Solve [ x 2 ]+ [ x 3 ]= 5 x 6 .
• The largest interval lying in (- 2 , 2 ) for which the function f(x)=4^ -x^ 2 + ^ -1 ( x 2 -1 ) + log (cos x) is…
• If S is the set of all real x such that 2 x+1 2 x^ 3 +3 x^ 2 +x is positive, then S contains
• If x 2 + 6x – 27 > 0 and x 2 – 3x – 4 < 0, then
• The function f(x) = log (x+ x^ 2 +1 ) , is a/an
• Let f : R → R be a function such that f (x) = x 3 + x 2 + 3x + sin x. Then
• The domain of the function is
• The number of real solutions of the equation 1 + |e x - 1| = e x (e x - 2) is :
• Let f(x)=x^ 3 +3 be bijective function, find its inverse
• Given : y=2[x]+3 and y=3[x-2]+5 , then find value of [ x + y ]
• Let M and m respectively be the maximum and minimum values of the function f ( x ) = tan –1 (sin x + cos x ) in [0, 2 ]…
• Given below are two statements. One is labelled as Assertion and the other is labelled as Reason. STATEMENT - 1…
• A = 1, 2, 3, 4 , B = 1, 2, 3, 4, 5, 6 are two sets, and function f: A B is defined by f(x)=x+2 ∀ x ∈ A, then the…
• If f( x )= 1 1- x , then the derivative of the composite function f[f f(x) ] is equal to :
• If f(x)= [ ] x+ [ x], where [y] is the greatest integer function of y, then f ( 2 ) is equal to
• Find the solution set of [ x ^ 2 ]+( x +1)^ 2 =25 , where [x] is the least integer greater than or equal to x
• If f(x) is a polynomial function satisfying f(x) f ( 1 x )=f(x)+f ( 1 x ) and f(3)=28 . Find f(4)
• Solve for x : 3^ ( x ^ 2 -2 ) < ( 1 3 )^ (1- 3 2 | x | )
• The domain of the function f(x)= 1 [x]^ 2 -[x]-6 where [ ] denotes greatest integer function
• Find the domain of f(x)= 1 x-5 +x^ 2 + 1 x+7
• cos [tan –1 sin (cot –1 x) ] is equal to :
• The graph of the function y=f(x) is symmetrical about the line y=2 , then
• Given the sets A = 1, 2, 3 , B = 3, 4 , C = 4, 5, 6 , then is
• Let D be the domain of the function f(x)= ^ -1 ( _ 3 x ( 6+2 _ 3 x -5 x ) ) . If the range of the function g : D → R…
• A mapping f: N N , where N is the set of natural numbers is defined as f(n)=n^ 2 , for n odd f(n)=2 n+1 , for n even…
• The range of f(x)=4 ^ -1 ( x^ 2 x^ 2 +1 ) is
• If g f (x) = |sin x| and f g (x) = ( x )^ 2 , then
• Let f be a function from R to R given by f (x) = x^ 2 -4 x^ 2 +1 . Then f (x) is.
• Let A = R - 3 , B = R - 1 , Let f : A → B be defined by f(x) = x-2 x-3 , then
• The value of [ 2 - ^ -1 (- 3 2 ) ] is :
• If e x + e f (x) = e, then range of the function of f is
• If A = 1, 2, 3, 4 , B = 2, 3, 5, 6 and C = 3, 4, 6, 7 , then
• If the domain of the function f ( x ) = ^ -1 ( x-1 2 x+3 ) is R -( , ) , then 12 is equal to :
• If ^ -1 ( a x )+ ^ -1 ( ~b x )= 2 , then x is equal to :
• Let A = [–1, 1] and f : A → A be defined as f (x) = x |x| for all x ∈ A, then f (x) is
• The range of the function f( x )= x ^ 2 + 1 x ^ 2 +1
• Let f be a real valued function satisfying f (x + y) = f (x) f (y) for all x, y ∈ R such that f (1) = a. Then, f (x) =
• The inverse function of f(x)= 8^ 2 x -8^ -2 x 8^ 2 x +8^ -2 x , x (-1,1) , is
• Let f( x )= x x +1 , x -1 . Then, for what value of II is f(f(x))=x ?
• The function f(x)= [ (x+ 1+x^ 2 ) ] is
• If f ( x )= 1 | x |- x , then domain of f (x) is
• If n (A) = 110, n (B) = 300 and n (A - B) = 50 then n (A ∪ B) equals
• Let the function f. g. h are defined from the set of real numbers R to R such that f(x)=x^ 2 -1 g(x) = (x^ 2 +1 ) and…

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