If you want it short and simple:
f^-1 = x^3 + 5
If you wanna stay for the ride:
f(x) is basically a fancy way of saying y. So we are solving for the inverse of
y = ^3 sqrt x - 5 (the cube root of x - 5). When solving an inverse, just simply swap the x's and y's!. This'll make x = ^3 sqrt y - 5, or the cube root of y - 5.
Now that all that is over with, we solve:
Remember, our new equation is
x = ^3 sqrt y - 5
To get rid of the annoying radical, cube both sides, or add a power of 3 to both sides.
x^3 = y - 5
Squaring a square root or cubing a cube root will always get
rid of the radical.
Now it's just the basic stuff:
+ 5 x^3 = y - 5 + 5 (add 5 to both sides)
Don't forget to change "y" to f^-1!
Your answer is f^-1 = x^3 + 5, or option A.
NOTE: f^-1 is fancy for the inverse. It basically means the same thing as "y". y = x^3 + 5 means the same thing.
An easy step-by-step list of what to do in inverse problems:
1. Switch f(x) to y (this just helps keep things lookin' simple)
2. swap x and y values (ex: y=2x would become x=2y)
3. SOLVE! (use your algebra tools)
If there is any confusion then please comment! I'd love to help!
