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