Question 377442
I will assume that {{{f(x) = x^3/2 - 7}}}.  This function is one-to-one, and so it will have an inverse function.
Then {{{y = x^3/2 - 7}}}.  Interchange the places of x and y:
{{{x = y^3/2 - 7}}}.  Then solve for y in terms of x.
{{{2(x+7) = y^3}}}.
{{{2x+14 = y^3}}},
{{{y = root(3, 2x+14)}}}.  This is the inverse function.