- #1

Jet1045

- 49

- 0

## Homework Statement

Hello! I am having troubles with a question I just got in my AP calc class. It is:

Let f(x) = x

^{5}+ 2x

^{3}+ x + 1

a) find f

^{-1}(3) and (f

^{-1})'(3)

## Homework Equations

N/A

## The Attempt at a Solution

Okay so my first idea was obviously to switch the x and y in f(x) giving me x = y

^{5}+ 2y

^{3}+ y + 1 however, it is clearly too difficult to isolate y in this equation.

So i was thinking, for f

^{-1}(3) , if I substitute 3 for y in the original equation, giving me 3 = x

^{5}+ 2x

^{3}+ x + 1 and solve for the zeroes, will that give me my answer to f

^{-1}(3) ? And then for (f

^{-1})'(3), i would set the derivative of f(x) to 3, and solve for the zeroes, which would look like 3 = 5x

^{4}+ 6x

^{2}+ 1

Would doing these things with f(x) effectively give me the answers to these two inverse problems?

Any help would be appreciated :)