A easy function

Level pending

If f f (2 x x ) = 2 2 + x \frac{2}{2 + x} for all x x > 0, find 2 f f ( x x ).

(A). 2 1 + x \frac{2}{1 + x} (B). 2 2 + x \frac{2}{2 + x} (C). 4 1 + x \frac{4}{1 + x} (D). 4 2 + x \frac{4}{2 + x} (E). 8 4 + x \frac{8}{4 + x}

E C A B D

Ricky Huang by Ricky Huang , 17, China

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1 solution

Ricky Huang
May 13, 2020

Let y y = 2 x x => x x = y 2 \frac{y}{2} .

f ( 2 x ) f(2x) = 2 2 + x \frac{2}{2 + x} => f ( y ) f(y) = 2 2 + 0.5 y \frac{2}{2 + 0.5y} = 4 4 + y \frac{4}{4 + y} => f ( x ) f(x) = 4 4 + x \frac{4}{4 + x} . 2 f ( x ) 2f(x) = 2 * 4 4 + x \frac{4}{4 + x} = 8 4 + x \frac{8}{4 + x} .

So the answer is (E).

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