Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2023MathematicsFunctions

If 2 f (x^2 )+3 f ( 1 x^2 )=x^2-1, x R- 0 , then f (x^8 ) is equal to

Options

  1. A(1-x^8 ) (2 x^8+3 ) 5 x^8
  2. B(1+x^8 ) (2 x^8-3 ) 5 x^8
  3. C(1-x^8 ) (2 x^8-3 ) 5 x^8
  4. DNone of these

Correct answer

A. (1-x^8 ) (2 x^8+3 ) 5 x^8

Step-by-step solution

Replacing x by 1 x , we get On multiplying Eq. (i) by 2, Eq. (ii) by 3 and then subtracting Eq. (i) from Eq. (ii), we get array rlrl & & 5 f (x^2 ) & =3 ( 1 x^2 -1 )-2 (x^2-1 ) & 5 f (x^2 ) & = 3 x^2 -2 x^2-1 & f (x^2 ) & = 1 5 ( 3 x^2 -2 x^2-1 ) & f (x^2 ) & = 1 5 x^2 (3-2 x^4-x^2 ) & f (x^2 ) & = (2 x^2+3 ) (1-x^2 ) 5 x^2 & & f (x^8 ) & = (1-x^8 ) (2 x^8+3 ) 5 x^8 array

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 COMEDK PYQs