## anonymous one year ago help on finding inverse functions! f(x) = x^3 - 8

1. IrishBoy123

write it as $$y = x^3 - 8$$ ad then find $$x = \ ...$$ in terms of y

2. anonymous

i know how to do that, i added 8 to both sides but im stuck on what to do with the cubed x

3. tkhunny

Have you considered a Cube Root?

4. anonymous

whats that

5. IrishBoy123

$$\sqrt[3]{27} = 3$$ because $$3 \times 3 \times 3 = 27$$

6. IrishBoy123

$$\sqrt[3]{whatever}$$ is the cube root of whatever

7. anonymous

oh, so it would be f^-1 (x) = 3√x + 8 with the radical going over both x and 8 or just x?

8. tkhunny

Pretty much. Or, you can use a 1/3 exponent.

9. anonymous

its a one-to one function right

10. tkhunny

In this case, it is.

11. anonymous

im confused because i know its one of the 2 choices, both have f(-1)x = 3√x + 8, but one has the radicand or whatever its called over the x ONLY, and the other has the radicand over the whole expression (x+8) which one is it?

12. anonymous

13. tkhunny

You should not be confused. Many exams have fake answers that might be plausible on first inspection. You must pick the right one.

14. anonymous

its the one i picked

15. anonymous

with the radicand going over the whole thing

16. tkhunny

If you took the cube root of the whole thing, then yes. Did you?

17. anonymous

no only for x^3

18. tkhunny

$$y = x^{3} - 8$$ Swap $$x = y^{3} - 8$$ Solve $$x + 8 = y^{3}$$ $$\sqrt[3]{x + 8} = y$$ Watch yourself work. Don't guess.