Answer
$\mathrm{See\:the\:table\:below.}$
Work Step by Step
$d.\quad (f\circ g)(x)=f(g(x))$
$=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-1}\ =\ \frac{\frac{x}{x-1}}{\frac{x-x+1}{x-1}}$
$=\frac{\frac{x}{x-1}}{\frac{1}{x-1}}=x$
$e.\quad$ Let's say $\ g(x)=y$. Then our composite function is given as:
$(f\circ g)(x)=f(g(x))$
$f(y)=1+\frac{1}{y}$
$x=1+\frac{1}{y}$
Solve this equation for $\ y\ $ which will give us the value of $\ g(x).$
$xy=y+1$
$y(x-1)=1$
$y=\frac{1}{x-1}$
$g(x)=\frac{1}{x-1}$
