# Finding the inverse of a function?

1. Nov 19, 2012

### nukeman

Finding the inverse of a function???

1. The problem statement, all variables and given/known data

Find (f^-1)'(a), a =2

√(x^3 + x^2 +x +1)

So, if a = 2, then f^-1(2) = 1 and f(1) = 2

2. Relevant equations

3. The attempt at a solution

I figured out that f(1) = 2,

so

√(3(1)^2 + 2(1) + 1)

= √6

so the final answer I got was 1/√(6)

?

2. Nov 19, 2012

### Staff: Mentor

Re: Finding the inverse of a function???

They are not asking for f-1(2) -- you need to get (f-1)'(2).

Start by differentiating each side with respect to x to eventually end up with y = (f-1)'(x).

3. Nov 19, 2012

### nukeman

Re: Finding the inverse of a function???

I dont understand. What is the first thing I do?

Would it be to figure out what value of f(x) would equal 2?

In this case, 1 would correct?

4. Nov 19, 2012

### Staff: Mentor

Re: Finding the inverse of a function???

I don't think this is relevant in this problem. They are asking you about the derivative of the inverse, not the inverse.

5. Nov 19, 2012

### gopher_p

Re: Finding the inverse of a function???

He's trying to use $(f^{-1})'(a)=\frac{1}{f'(f^{-1}(a))}$.

6. Nov 19, 2012

### nukeman

Re: Finding the inverse of a function???

Correct, I am

7. Nov 19, 2012

### gopher_p

Re: Finding the inverse of a function???

So then $(f^{-1})'(2)=\frac{1}{f'(f^{-1}(2))}=\frac{1}{f'(1)}=\ldots$

Find $f'(1)$ and you're done.

Edit: I now see where you tried to do this. Maybe take your time with that derivative. You need to use the power rule and the chain rule.

P.S. I reckon $(f^{-1})'(a)=\frac{1}{f'(f^{-1}(a))}$ is a fairly relevant equation here. Probably shoulda put that in the first post. You can't assume that tutors remember everything from their undergrad (maybe even high school) calc course.

8. Nov 19, 2012

### nukeman

Re: Finding the inverse of a function???

I dont understand how the answer is 2/3 :(

9. Nov 19, 2012

### gopher_p

Re: Finding the inverse of a function???

Three questions:

1) What is the derivative (with respect to $x$) of $\sqrt{x}$? (hint: you need the power rule)

2) Assuming $u$ is a differentiable function of $x$, what is the derivative with respect to $x$ of $\sqrt{u}$? (hint: you need the chain rule)

3) What is the derivative of $\sqrt{x^3 + x^2 +x +1}$? (hint: let $u=x^3 + x^2 +x +1$ and use part 2)

10. Nov 19, 2012

### Dick

Re: Finding the inverse of a function???

Maybe that's because you haven't worked out what f' is. Do that and then figure out what 1/f'(1) is.