Question

Question in Finding rule for inverse function

http://img190.imageshack.us/img190/9075/andysnap007.png

Answer 1

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,\[2(g(x))^{1/3}+8=x \rightarrow 2(g(x))^{1/3}=x-8\]

Answer 2

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

Answer 3

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

Answer 4

Just did it.

Answer 5

It's on your list too.

Answer 6

Thank you so much

Answer 7

:)

Answer 8

Become a fan ;)

Answer 9

okai :)