Question 956968
Yes, 
{{{f(x)=1/x}}}} has an inverse of
{{{f^(-1)(x)=1/x}}} so 
{{{f^(-1)(f(x))=1/f=1/(1/x)=x}}}
So the inverse is the reciprocal of the function.
Example:
{{{f(2)=0.5}}}
{{{f^(-1)(0.5)=2}}}
{{{f^(-1)(f(2))=f^(-1)(0.5)=2}}}
So {{{f^(-1)(f(x))=x}}} by definition, an inverse.