Let f (x) be invertible function and let f –1 (x) be its inverse. Let equation f f –1 (x)…
Mathematics · JEE Advanced · NTA Exams — Sets, Relations and Functions
Let f (x) be invertible function and let f –1 (x) be its inverse. Let equation f { f –1(x)} = f –1(x) has two real roots α and β (within domain of f (x)), then
- f (x) = x, also have same two real roots.
- f –1(x) = x, also have same two real roots.
- f (x) = f –1(x), also have same two real roots.
- Area formed by (0, 0) (α, f (α)) and (β, f (β)) is 1 unit.
Answer
(A) f (x) = x, also have same two real roots., (B) f –1 (x) = x, also have same two real roots., (C) f (x) = f –1 (x), also have same two real roots.
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The function f : R → R defined by f ( x ) = 6 x + 6 |x| is
- Let f ( x ) be defined for all x > 0 and be continuous. If f ( x ) satisfy f ( x y ) = f ( x ) – f ( y ) for…
- If log 0.3 ( x – 1) 0.09 ( x – 1), then x lies in the interval
- Assertion : Let f (x) be a function satisfying f (x – 1) + f (x + 1) = 2 f (x) for all x ∈ R. Then f (x) is…
- The function f ( x ) = [ x ] 2 – [ x 2 ] (where [ y ] is the greatest integer less than or equal to y ) is…
- Let f(x)= ( 6 ( 2 x ) ) for all x ∈ R and g(x)= 2 x for all x ∈ R . Let ( fog )( x ) denote f ( g ( x )) and…
- If graph of y = f ( x ) is Then f ( x ) can be
- A rational function is defined as quotient of two polynomials, p( x ) and q( x ). The domain of the rational…
More Sets, Relations and Functions questions · Browse all practice questions