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Quantitative Aptitude Question on Functions

The functions f(x) and g(x) are related as f(g(x)) = xg(f(f(x))), where f (x) = xx−1\frac{x}{x-1}. What could be the functional form g(x)?

A

1x\frac{1}{x}

B

xx+1\frac{x}{x+1}

C

x+1x\frac{x+1}{x}

D

xx−1\frac{x}{x-1}

E

x1−x\frac{x}{1-x}

Answer

x+1x\frac{x+1}{x}

Explanation

Solution

The correct option is (C): x+1x\frac{x+1}{x}