## anonymous one year ago Find the inverse of the function. f(x) = the cube root of quantity x divided by nine. - 4

1. anonymous

@Jack1

2. Jack1

$$\Large f(x)=\sqrt[3]{ \frac x9}-4$$ make f(x) = y $$\Large y=\sqrt[3]{ \frac x9}-4$$ swap x and y terms $$\huge \color{red}x=\sqrt[3]{ \frac {\color{red}y}9}-4$$ now put x in terms of y $$\Large x=\sqrt[3]{ \frac y9}-4$$ $$\Large x+4=\sqrt[3]{ \frac y9}$$ $$\Large (x+4)^3=\frac y9$$ $$\Large 9(x+4)^3=y$$ $$\Large 9(x+4)^3=f^{-1}(x)$$ $$\Large f^{-1}(x) = 9(x+4)^3$$ does this make sense @PHUNISH ?

3. anonymous

Ohh yeah for some reason I kept cubing the x idk how or why thanks though!

4. Jack1

np dude ;)

5. anonymous

I have a couple more I got wrong if you could explain them to me, ill tag you in them

6. Jack1

cools ;)