what-is-domain-of-x-for-f-x-2f-1-x-x-2-

Question Number 85233 by jagoll last updated on 20/Mar/20

what is domain of x for

f (x) + 2 f (1 - x) = x^{2}

Commented by jagoll last updated on 20/Mar/20

replace 1 - x by x

f (1 - x) + 2 f (x) = {(1 - x)}^{2} (ii)

multiply by 2 eq (ii)

4 f (x) + 2 f (1 - x) = {2 x}^{2} - 4 x + 2

f (x) + 2 f (1 - x) = x^{2}

(ii) - (i)

3 f (x) = x^{2} - 4 x + 2

f (x) = \frac{x^{2} - 4 x + 2}{3}, \forall x \in R

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