#### Answer

See the verification below.

#### Work Step by Step

The functions $f(x)$ and $g(x)$ are known as inverse functions. Thus, we simplify
$(f\circ g) (x)=(g\circ f) (x)$ or, $f[g(x)]=g[f(x)]$
as follows:
$(f\circ g) (x) =f[g(x)]=f [\dfrac{1}{x}]=\dfrac{1}{1/x} =x$
and
$(g\circ f) (x) = g[f(x)]=g(1/x)=\dfrac{1}{1/x}=x$
Hence, verified.