Question 440054
Replace x by {{{f^(-1)(x)}}}
==>  {{{f(f^(-1)(x)) = 2*f^(-1)(x) - 1}}}
<==> {{{x = 2*f^(-1)(x) - 1}}}
==> {{{f^(-1)(x) = (x+1)/2}}}

{{{graph( 300, 300, -5, 5, -5, 5, (x +1)/2, 2x-1 )}}}