One more before I go and finish Math...
the function f is one-to-one. Find its inverse

f(x)=(x+2)^3-8

I need to know how it is done step by step because it will be on my final, I'm sure, thanks! :)

Question

One more before I go and finish Math...
the function f is one-to-one. Find its inverse

f(x)=(x+2)^3-8

I need to know how it is done step by step because it will be on my final, I'm sure, thanks! :)

anonymous · Answer

I will give a medal

kmeis002 · Answer

An inverse is a function (mapping) that takes the Range and maps it back into its corresponding Domain. A common trick is to do switch the x and y and solve again for y, or you can just solve for x.

$$ x = (y+2)^3 - 8  \ x+8 = (y+2)^3 = (x+8)^\frac{1}{3} = y + 2 \ y = (x+8)^\frac{1}{3} - 2 \ f^{-1} (x)=(x+8)^\frac{1}{3} $$

anonymous · Answer

what happened to the -2?

kmeis002 · Answer

typo, sorry abou that, it should be
$$ f^{-1}(x) = (x+8)^{\frac{1}{3}} -2$$

anonymous · Answer

You got your medal, well deserved and thorough too! Thanks for all! :)