Confusion with Inverse Functions AP Calc

[Loppyfoot]

Homework Statement

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)

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

 

[VeeEight]

Your first step would be to find the inverse function and then to plug in the required number. Here's a link: http://www.analyzemath.com/inversefunction/Tutorials.html

 

[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??

 

[Mark44]

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

 

[Loppyfoot]

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

 

[Mark44]

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.