Question 390149
For:
{{{y = x^3+1 }}} find {{{f^(-1)(x)}}} Exchange the x and y.
{{{x = y^3+1}}} Solve for y.
{{{y^3 = x-1}}} Take the cube root of both sides.
{{{y = (x-1)^(1/3)}}} Replace the y with {{{f^(-1)(x)}}}
{{{f^(-1)(x) = (x-1)^(1/3)}}}
Check to see that:
{{{f(f^(-1)(x)) = x}}}
{{{f(f^(-1)(x)) = f((x-1)^(-1/3))}}}={{{((x-1)^(1/3))^3+1 = (x-1)+1}}}={{{x}}}