help on finding inverse functions!

f(x) = x^3 - 8

Question

help on finding inverse functions!

f(x) = x^3 - 8

irishboy123 · Answer

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

anonymous · Answer

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

tkhunny · Answer

Have you considered a Cube Root?

anonymous · Answer

whats that

irishboy123 · Answer

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

irishboy123 · Answer

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

anonymous · Answer

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

tkhunny · Answer

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

anonymous · Answer

its a one-to one function right

tkhunny · Answer

In this case, it is.

anonymous · Answer

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?

anonymous · Answer

attachment

tkhunny · Answer

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

anonymous · Answer

its the one i picked

anonymous · Answer

with the radicand going over the whole thing

tkhunny · Answer

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

anonymous · Answer

no only for x^3

tkhunny · Answer

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