Question 106807
Find the inverse and verify:
{{{f(x) = x^3+1}}} Change the f(x) to y, then interchange the x and y.
{{{y = x^3+1}}}
{{{x = y^3+1}}} Now solve this for y.
{{{y^3 = x-1}}} Take the cube root of both sides.
{{{y = (x-1)^(1/3)}}} Now change the y to {{{f^(-1)(x)}}}.
{{{f^(-1)(x) = (x-1)^(1/3)}}}
Check:
Show 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