A function f from a set X to Y is called onto, if for every y ∈ Y there exist x ∈ X such…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
A function f from a set X to Y is called onto, if for every
y ∈ Y there exist x ∈ X such that f (x) = y. Unless the contrary is specified, a real function is onto if it takes all real values, otherwise it is called into function. Thus, if X and Y are finite sets, then f cannot be onto If Y contains more element than X.
Which of the following is not true ?
- A one-one function from the set {a, b, c} to {α, β, γ}
is onto also. - An onto function from an infinite set to a finite set
cannot be one-one. - An onto function is always invertible.
- The function tan x and cot x are onto
Answer
(C) An onto function is always invertible.
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Let function f : R → R be defined by f ( x ) = 2 x + sin x for x ∈ R . Then f is
- Let f ( x ) = [ x ] = the greatest integer less than or equal to x and g ( x ) = x – [ x ]. Then for any two…
- Let f(x)= x x+1 , x ≠ –1, then for what value of α is f ( f ( x )) = x ?
- The function f (x) = ( x) + sin –1 ( 1+x^ 2 2 x ) is defined for :
- If f(x)= 4^ x 4^ x +2 then f ( 1 1997 )+f ( 2 1997 )+ .+f ( 1996 1997 ) is equal to
- Let f ( x ) = x 2 and g ( x ) = sin x for all x ∈ R . Then the set of all x satisfying ( fogogof )( x ) = (…
- Let y 1 : [0, ∞) R , y 2 : [0, ∞ ] R , f : [0, ∞) R , and g : [0, ∞] R , be functions such that f (0) = g (0)…
- If | x – 1| + | x | + | x + 1| > 6 ; then x lies in
More Sets, Relations and Functions questions · Browse all practice questions