Answer
$f[g(x)]=\sqrt{\dfrac{x-1}{x}}$
$g[f(x)]=\displaystyle \frac{-1}{\sqrt{x+1}}$
Work Step by Step
In the expression for f(x), replace x with g(x)
$f[g(x)]=\sqrt{g(x)+1}$
$=\sqrt{\dfrac{-1}{x}+1}$
$=\sqrt{\dfrac{x-1}{x}}$
In the expression for g(x), replace x with f(x)
$g[f(x)]=\displaystyle \frac{-1}{f(x)}$
$=\displaystyle \frac{-1}{\sqrt{x+1}}$
