MHT CET202016 Oct 2020Morning ShiftMathematicsFunctionsActual

If f(x)= 2 x+3 3 x-2 , x 2 3 , then the function fof is

Options

Aan even function
Ban identity function
Ca constant function
Dan exponential function

Correct answer

B. an identity function

Step-by-step solution

(B) f f=f(f(x)) aligned =& 2 ( 2 x+3 3 x-2 )+3 3 ( 2 x+3 3 x-2 )-2 = 4 x+6 3 x-2 +3 6 x+9 3 x-2 -2 =& 4 x+6+9 x-6 6 x+9-6 x+4 = 13 x 13 =x aligned Therefore, we can say that the composite function for for given function is an identity function.

Practice Functions on Quantrex Academy →

More from Functions

If f : R A , defined by f ( x )= x + 3 x -1 , is an onto function then A = 2025 Let g(x)=1+x-[x] and f(x)= cases -1, & x 0 cases ([x] ) denotes the greatest integer less than or equal to (x ). Then for all x , f ( g ( x ))= 2025 The domain of the real valued function f(x)= 3 4-x^2 + ₁₀ (x^3-x ) is 2025 A real valued function f: A B defined by f(x)= 4-x^2 4+x^2 x A is a bijection. If -4 A then A B= 2025 Let [ x ] represent the greatest integer less than or equal to x , x = x -[ x ] , 2 =1.414 and 3 =1.732 . If f(x)= x+ [ x 1+x^2 ] is a real valued function, then f ( 2 )+ f (- 3 )= 2025 If the range of the function f(x)=-3 x-3 is 3,-6,-9,-18 , then which one of the following is not in the domain of f ? 2025 The domain of the function f(x)= _e ( 1 x^2-4 x+4 ) + ⁻¹ (x^2-2 ) is 2025 Consider the following statements Statement-I : A function f : A B is said to be one-one if and only if f(x) f(y) x y Statement-II : A relation f: A B is said to be a function if x 2025 Full Functions list All MHT CET PYQs