Answer
(a.)$(f\circ g)(x) =x$.
(b.)$(g\circ f)(x) =x$.
(c.)$(f\circ g)(2) =2$.
Work Step by Step
The given functions are
$f(x)=\frac{1}{x}$ and $g(x)=\frac{1}{x}$.
(a) $(f\circ g)(x) = f(g(x))$
Replace $x$ with $g(x)$ in the function $f(x)$.
$f(g(x))=\frac{1}{g(x)}$
Plug value of $g(x)$ in the right hand side.
$f(g(x))=\frac{1}{\frac{1}{x}}$
$f(g(x))=x$.
Hence, $(f\circ g)(x) =x$.
(b) $(g\circ f)(x) = g(f(x))$
Replace $x$ with $f(x)$ in the function $g(x)$.
$g(f(x))=\frac{1}{f(x)}$
Plug value of $f(x)$ in the right hand side.
$g(f(x))=\frac{1}{\frac{1}{x}}$
$g(f(x))=x$.
Hence, $(g\circ f)(x) =x$.
(c) Replace $x$ with $2$ in the part (a) solution.
$(f\circ g)(2) =2$.