Question
Question: If f(x) + 2f(1 - x) = x<sup>2</sup> +1 ∀ x ∈ R then f(x) is...
If f(x) + 2f(1 - x) = x2 +1 ∀ x ∈ R then f(x) is
A
31 (x2 + 4x - 3)
B
32 (x2 + 4x – 3)
C
31 (x2 – 4x + 3)
D
32 (x2 – 4x + 3)
Answer
31 (x2 – 4x + 3)
Explanation
Solution
f(x) + 2f(1 - x) = x2 + 1
Replacing x → (1 - x) we get; f(1 – x) + 2f(x) = (1 -x)2+ 1
⇒ f(1 - x) + 2f(x) = 2 + x2 - 2x
From these equations we get f(x) = 31 (x2 - 4x + 3)