How to Find the Inverse of a Polynomial: Step-by-Step Guide

[HopelessCalc]

Homework Statement

Let f(x) = 2x^3 + 5x + 3
Find the inverse at f^-1(x) = 1

Homework Equations

N/A

The Attempt at a Solution

The only way that I know how to solve inverses is by solving for X, then replacing it by Y. Then I supposed I would sub 1 into the inverted polynomial. However I'm not sure how to solve for X.
My attempt:
y - 3 = 2x^3 + 5x
(y - 3)/x = x(2x^2 + 5)

Then, hopelessness. Any info will be extremely helpful for my test this Friday. Thank you.

 

[dynamicsolo]

Your statement is a bit unclear -- I'm interpreting you to say that you want to find x = f^-1(1) , that is, what value of x gives f(x) = 1 ?

I don't think they want you to solve the cubic equation 2x^{3} + 5x + 3 = 1 (unless they taught you how to do so in your course). This doesn't come out nicely at all...

I'm wondering if they're asking that if you had the function y = f^-1(x)*, what value of x would give y = 1 ? This is equivalent to asking what f(1) equals: the value of f(1) is the number that f^-1(x) would "take back" to 1 .*whatever that is exactly -- it wouldn't be pretty; instead, we will work with what is called the "implicit function"

 

[abhishek ghos]

buddy think again;
the answer is f(1)...

 

[HallsofIvy]

Yes, as both dynamicsolo and abhishek ghos are saying, you are completely misunderstanding the problem. The problem does NOT as you to find the inverse function, which would be extremely complex. It only asks you to find the single value f^{-1}(1).

Use the fact that if f(x)= y then x= f^{-1}(y).