# Confusion with Inverse Functions AP Calc

1. Nov 11, 2009

### Loppyfoot

1. The problem statement, all variables and given/known data
1) Given f(x)= .01x³ + .7x -2 . Approximate ƒ−1(3).

2)Given f(x) = (x³) / (x²+1) and g(x) = ƒ–1(x). Evaluate g'(2)

3. The attempt at a solution

1) Would this be correct? 3=.01x^3 + .7x -2
But then, how would I find x at 3?

2) I am confused about going about solving this problem. Any help would be appreciated@!!

Thanks

2. Nov 11, 2009

### VeeEight

3. Nov 11, 2009

### Loppyfoot

OK, so for number one, I wouldn't just set the function equal to 3 and then solve?? And if I would do that how would I find x??

4. Nov 11, 2009

### Staff: Mentor

For #1, you're looking for a number x0 such that f(x0) $\approx$ 3. Equivalently, x0 $\approx$ f-1(3)

5. Nov 11, 2009

### Loppyfoot

So then I have 3=.01x^3 + .7x -2. What step would I take to solve this problem next?

6. Nov 11, 2009

### Staff: Mentor

How about adding 2 to both sides? This will give you .01x^2 + .7x = 5. At that point I would pick a value and put it in for x on the left side and see how close I got to 5. If the result is larger than 5, pick a smaller value and repeat the process so that you get closer and closer to 5 as the result.