Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2024MathematicsFunctions

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

Options

  1. A2-3 x
  2. B1 2 (2-3 x)
  3. C1 3 (2-3 x)
  4. D1 3 (2 x-3)

Correct answer

C. 1 3 (2-3 x)

Step-by-step solution

We have, f(x)+2 f(1-x)=x ...(i) Now, replace x by 1-x array r f(1-x)+2 f(1-(1-x))=1-x f(1-x)+2 f(x)=1-x ...(ii) array Multiply by 2 to the Eq. (ii) and subtract from Eq. (i), aligned & 2 f(1-x)+4 f(x)-f(x)-2 f(1-x)=2-2 x-x & 3 f(x)=2-3 x & f(x)= 1 3 (2-3 x) 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 COMEDK PYQs