Having trouble finding the derivative of an inverse function

[barryj]

Summary: Please see the attached problem and solution

The answer is 1/5. I have tried various solutions and cannot get 1/5.
What is my error?

[Moderator's note: Moved from a technical forum and thus no template.]

 

[hutchphd]

Carefully parse the question. It doesn't want the solution when x =2.

 

[barryj]

I am confused. I know I have f' correct as 3X^2 + 2

So, should I use 2 or 13? Neither gives me the supposedly correct answer(per the book) of 1/5

 

[hutchphd]

The argument of the inverse function is a =f(x).

 

[barryj]

OK, so a = 13. if I use 13 instead of 2 I still don't get the right answer.

F(2) = 13 so G(13) = 2.

 

[hutchphd]

Sorrry what is 13?

 

[barryj]

the inverse of F(2)

I have paralleled an example that is almost identical to this problem and I understand it. I think the answer is wrong.

 

[hutchphd]

The question wants the (inverse)' when f(x)=2.

 

[hutchphd]

There may be a cleverer way but what is x when f(x)=2??

 

[barryj]

1 so f(1) = 2 then g(2) = 1 and I get 1/5
I need to study futher to understand what is being asked.

 

[hutchphd]

So plug it in!
(and the term is derivative !)

 

[barryj]

Thanks