Question

If f is satisfied the condition 2f(x) + f(1 - x) = x², x ∈ R then f(x) = .....

(a) (x² + 2x - 1)/6

(b) (x² + 4x - 1)/3

(c) (x² + 2x - 1)/3

(d) (x² - 3x + 1)/6

Answer 1

The correct option (c) (x² + 2x - 1)/3

Explanation:

Here 2f(x) + f(1 – x) = x² ... ... ... (1) 

Now put 1 – x in place of x we get 

2f(1 – x) + f(x) = (1 – x)² ... ... ... (2) 

multiplying (1) and (2) we get f(x) = (x² + 2x - 1)/3