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! :)

Answer 1

I will give a medal

Answer 2

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.

\[ x = (y+2)^3 - 8 \\ x+8 = (y+2)^3 = (x+8)^\frac{1}{3} = y + 2 \\ y = (x+8)^\frac{1}{3} - 2 \\ f^{-1} (x)=(x+8)^\frac{1}{3} \]

Answer 3

what happened to the -2?

Answer 4

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

Answer 5

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