Question

Given the following functions f(x)

Answer 1

Answer:    x

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Work Shown:

$g(x) = \frac{(x-1)^2}{3}\\\\g(f(x)) = \frac{(f(x)-1)^2}{3}\\\\g(f(x)) = \frac{(1+\sqrt{3x}-1)^2}{3}\\\\g(f(x)) = \frac{(\sqrt{3x})^2}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x$

The idea is to start with g(x) and then replace every x with f(x). From there you plug in f(x) = 1+sqrt(3x) and simplify.