Answer
$a. -\frac{1}{3}$
$b. 2$
$c. \frac{-x}{x+1}$
$d. \frac{1}{x}$
$e. 0$
$f. \frac{3}{4}$
$g. x-2$
$h. \frac{x+1}{x+2}$
Work Step by Step
$f(x)=x-1$
$g(x)=\frac{1}{x+1}$
$a.\quad f(g(\frac{1}{2}))=?$
$f(g(\frac{1}{2}))=\frac{-\frac{1}{2}}{\frac{1}{2}+1}$
$=-\frac{1}{3}$
$b.\quad g(f(\frac{1}{2}))=?$
$g(f(\frac{1}{2}))=\frac{\ 1\ }{\frac{1}{2}}$
$=2$
$c.\quad f(g(x))=?$
$f(g(x))=\frac{1}{x+1}-1=\frac{1-x-1}{x+1}$
$=\frac{-x}{x+1}$
$d.\quad g(f(x))=?$
$g(f(x))=\frac{1}{(x-1)+1}=\frac{1}{x}$
$e.\quad f(f(2))=?$
$f(f(2))=2-2=0$
$f.\quad g(g(2))=?$
$g(g(2))=\frac{3}{4}$
$g.\quad f(f(x))=?$
$f(f(x))=(x-1)-1=x-2$
$h.\quad g(g(x))=?$
$g(g(x))=\frac{1}{(\frac{1}{x+1})+1}$
$=\frac{x+1}{x+2}$
