anonymous
  • anonymous
help on finding inverse functions! f(x) = x^3 - 8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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IrishBoy123
  • IrishBoy123
write it as \(y = x^3 - 8\) ad then find \(x = \ ...\) in terms of y
anonymous
  • anonymous
i know how to do that, i added 8 to both sides but im stuck on what to do with the cubed x
tkhunny
  • tkhunny
Have you considered a Cube Root?

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anonymous
  • anonymous
whats that
IrishBoy123
  • IrishBoy123
\(\sqrt[3]{27} = 3\) because \(3 \times 3 \times 3 = 27\)
IrishBoy123
  • IrishBoy123
\(\sqrt[3]{whatever}\) is the cube root of whatever
anonymous
  • anonymous
oh, so it would be f^-1 (x) = 3√x + 8 with the radical going over both x and 8 or just x?
tkhunny
  • tkhunny
Pretty much. Or, you can use a 1/3 exponent.
anonymous
  • anonymous
its a one-to one function right
tkhunny
  • tkhunny
In this case, it is.
anonymous
  • 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?
anonymous
  • anonymous
tkhunny
  • tkhunny
You should not be confused. Many exams have fake answers that might be plausible on first inspection. You must pick the right one.
anonymous
  • anonymous
its the one i picked
anonymous
  • anonymous
with the radicand going over the whole thing
tkhunny
  • tkhunny
If you took the cube root of the whole thing, then yes. Did you?
anonymous
  • anonymous
no only for x^3
tkhunny
  • 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.

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