1. ## find inverse function

$\displaystyle f(x) = 5(x-2)^3 - 6$

Could someone help me find the inverse function for this function?

I understand these steps:

Set f(x) to y
$\displaystyle y = 5(x-2)^3 - 6$

Swap x and y
$\displaystyle x = 5(y-2)^3 - 6$

I think I'm supposed to solve for Y, but I'm not sure how to continue.

2. Originally Posted by absvalue
$\displaystyle f(x) = 5(x-2)^3 - 6$

Could someone help me find the inverse function for this function?

I understand these steps:

Set f(x) to y
$\displaystyle y = 5(x-2)^3 - 6$

Swap x and y
$\displaystyle x = 5(y-2)^3 - 6$

I think I'm supposed to solve for Y, but I'm not sure how to continue.
$\displaystyle x = 5(y-2)^3 - 6$

add 6 to both sides ...

$\displaystyle x+6 = 5(y-2)^3$

divide both sides by 5 ...

$\displaystyle \frac{x+6}{5} = (y-2)^3$

take the cube root of both sides ...

$\displaystyle \sqrt[3]{\frac{x+6}{5}} = y-2$

add 2 to both sides ...

$\displaystyle \sqrt[3]{\frac{x+6}{5}} + 2 = y$

you're done.

3. $\displaystyle x = 5(y-2)^3 - 6$

So far you are right. Like you said, you need to solve for y, and you just need some basic algebra to do that.

$\displaystyle x + 6 = 5(y-2)^3$

4. hi
$\displaystyle (y-2)^{3}=\frac{x+6}{5}\Leftrightarrow y-2=\sqrt[3]{\frac{x+6}{5}}\Leftrightarrow y= \sqrt[3]{\frac{x+6}{5}}+2$,now change $\displaystyle y$ to $\displaystyle f^{-1}(x)$