Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202310 May 2023Morning ShiftMathematicsFunctionsActual

f: R R ; g: R R are two functions such that f (x)=2 x-3, ~g (x)=x^3+5 , then (f g)⁻¹(-9) is

Options

  1. A-2
  2. B2
  3. C- 2
  4. D2

Correct answer

A. -2

Step-by-step solution

We have, f (x)=2 x-3, ~g (x)=x^3+5 aligned fog (x) & = f ( g (x)) & =2 ~g (x)-3 & =2 (x^3+5 )-3=2 x^3+7 aligned Let (f g)(x)=y=2 x^3+7 aligned & y=2 x^3+7 & y-7=2 x^3 & x^3= y-7 2 & x= ( y-7 2 )^ 1 3 & ( fog )⁻¹(y)= ( y-7 2 )^ 1 3 & ( fog )⁻¹(-9)= ( -9-7 2 )^ 1 3 =(-8)^ 1 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