what is the inverse of f if f (x) = ^3 sqrt x-7

the inverse of the function given will be:
f(x)=(x-7)^(1/3)
to get the inverse we make x the subject
let f(x)=y=(x-7)^(1/3)
y=(x-7)^(1/3)
getting the cube of both sides we have:
y³=[(x-7)^(1/3)]³
y³=x-7
thus
x=y³+7
next we replace y by x and x with f^-1(x)
thus the inverse will be:
f^-1(x)=x³+7