## anonymous 5 years ago Question in Finding rule for inverse function http://img190.imageshack.us/img190/9075/andysnap007.png

1. anonymous

You can find inverse functions using the definition. If f(x) is a function, and g(x) is its inverse, then$f(g(x))=g(f(x))=x$Now, you have$f(x)=2x^{1/3}+8$so that$f(g(x))=2(g(x))^{1/3}+8=x$Solving for g(x) gives,$2(g(x))^{1/3}+8=x \rightarrow 2(g(x))^{1/3}=x-8$

2. anonymous

I haven't practiced inverse functions. Thanks for the definition. So what happens next? How do we get the rule?

3. anonymous

Divide both sides by 2 and raise both sides to the power of 3,$2(g(x))^{1/3}=x-8 \rightarrow (g(x))^{1/3}=\frac{x-8}{2} \rightarrow g(x)=\left( \frac{x-8}{2} \right)^3$

4. anonymous

Just did it.

5. anonymous

6. anonymous

Thank you so much

7. anonymous

:)

8. anonymous

Become a fan ;)

9. anonymous

okai :)

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