Question 477888
You got to {{{x=(y-7)^3}}} okay.  Then you would have to solve for y.

Take the cube root of both sides:

{{{x^(1/3)=y-7}}}

And now add 7 to both sides:

{{{x^(1/3)+7=y}}}

Flip it for sanity's sake:

{{{y=x^(1/3)+7}}}

Now change y to f(x) and voila!!

Answer:
{{{f(x)=x^(1/3)+7}}}