inverse function

[ace123]

Hi i'm trying to remember inverse functions for calculus but i'm having a few problems. So any help would be appreciated.

f(x)= 2x^3 + 3x^2 + 7x+ 4

So I have no clue how to solve this for the inverse. I know how to do basic ones. But i've forgotten these kind. So can i just get a step in the right direction.

[Dick]

You can get an inverse expression for a general cubic only by using the cubic formula. I DON'T recommend this. It's too complicated. What's the actual problem you need to solve? You probably don't need an explicit formula.

[kuahji]

I'd agree, it would depend on the problem. You could use the cubic formula, but its pretty nasty.

[ace123]

Well I was hoping their was a nice way of doing b/c I knew about the cubic formula but wasn't about to use it for this. The actual question though was to find (f^-1)'(a) and the a= 4. I thought I had to find the inverse of the f(x) to solve the problem. Is there another way?

[Dick]

Yes there is. f^(-1)(f(x))=x. Differentiate both sides and use the chain rule. f^(-1)'(f(x))*f'(x)=1. So f^(-1)'(f(x))=1/f'(x). If you want to use this at f(x)=a=4, You still have to find a value of x such that f(x)=4. But that's a lot easier problem than finding the general inverse.

[ace123]

Oh, okay I see what your saying I didn't think about using f(x)=a=4. Thank you