What is the inverse of f if f(x)=^3 sqrt x-4

F(x)=^3 sqrt x-4 would be a bit clearer if you'd write it as f(x)=^3 sqrt(x-4) (that is, unless you really did mean f(x)=^3 sqrt(x) - 4  ).

1) replace "f(x)" with y:  f(x)=^3 sqrt(x-4)  =>   y=^3 sqrt(x-4)
2) interchange x and y:  x =

I stopped here after noticing your "^3".  "^3" cannot stand alone, as "^3" indicates exponentiation with power 3.  Did you mean x^3 or something else?

Please respond with clarification.  If you can, I'll try to help you finish this problem.

Move the decimal behind it