Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202012 Oct 2020Evening ShiftMathematicsFunctionsActual

If f(x)= 4 x+7 7 x-4 , then the value of f f[f(2)] =

Options

  1. A3 2
  2. B2 3
  3. C35 39
  4. D39 35

Correct answer

A. 3 2

Step-by-step solution

f(x)= 4 x+7 7 x-4 f(2)= 8+7 14-4 = 15 10 = 3 2 f[f(2)]=f ( 3 2 )= (4 3 2 )+7 (7 3 2 )-4 = 6+7 ( 21-8 2 ) = 13 2 13 =2f f[f(2)] =f(2)= 3 2 This problem can also be solved as follows : aligned f ( x ) = 4 x +7 7 x -4 & f [ f ( x )]= f [ 4 x +7 7 x -4 ] f [ 4 x +7 7 x -4 ] &= 4 ( 4 x +7 7 x -4 )+7 7 ( 4 x +7 7 x -4 )-4 &= 16 x +28+49 x -28 28 x +49-28 x +16 = 65 x 65 = x f f [ f ( x )] &= f x = 4 x +7 7 x -4 f f [ f (2)] &= 4(2)+7 7(2)-4 = 15 10 = 3 2 aligned

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 = 2025Let 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 ))= 2025The domain of the real valued function f(x)= 3 4-x^2 + ₁₀ (x^3-x ) is 2025A 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= 2025Let [ 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 )= 2025If 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 ? 2025The domain of the function f(x)= _e ( 1 x^2-4 x+4 ) + ⁻¹ (x^2-2 ) is 2025Consider 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