# Thread: Inverse Functions of polynomials

1. ## Inverse Functions of polynomials

Hey I was hoping you guys could help me out.

I have to find the inverse of

f(x)= 3 + x^2 + tan((y x pi)/2))

I know how to do inverses, but I cant figure out how to do them when its with polynomials. Anouther one I have that I can't figure out is:

f(x)= (e^x)/(1+2e^x)

and

f(x)=x^5+2x^3+3x+1

If anyone could help me with just a few of them, or give me an example of how to do one like this, Im sure i could figure the rest out.

Thanks for your time and help

2. If you know how to do inverses, then you know that the first step is replacing all instances of x with y and all instances of y with x. I will run through this problem with you: $y = \frac{e^x}{1+2e^x}$

First, switch x and y: $x = \frac{e^y}{1 + 2e^y}$

Then multiply both sides by $1 + 2e^y$: $x(1 + 2e^y) = e^y$

Distribute: $x + 2xe^y = e^y$

Subtract $2xe^y$ from both sides: $x = e^y - 2xe^y$

Factor: $x = e^y(1 - 2x)$

Divide both sides by $1 - 2x$: $\frac{x}{1-2x} = e^y$

Take the natural logarithm of both sides: $\ln{\frac{x}{1-2x}} = y$

And that's it.

3. Originally Posted by icemanfan
If you know how to do inverses, then you know that the first step is replacing all instances of x with y and all instances of y with x. I will run through this problem with you: $y = \frac{e^x}{1+2e^x}$

First, switch x and y: $x = \frac{e^y}{1 + 2e^y}$

Then multiply both sides by $1 + 2e^y$: $x(1 + 2e^y) = e^y$

Distribute: $x + 2xe^y = e^y$

Subtract $2xe^y$ from both sides: $x = e^y - 2xe^y$

Factor: $x = e^y(1 - 2x)$

Divide both sides by $1 - 2x$: $\frac{x}{1-2x} = e^y$

Take the natural logarithm of both sides: $\ln{\frac{x}{1-2x}} = y$

And that's it.
Thanks a lot I get it now, its pretty simple, but it wasn't before I saw how to do it lol.

Thanks again

4. ## Inverse polynomial function

Hi
I have read your response to finding an inverse function and it looks reasonably straight forward but was wondering whether you might be able to assist me in finding an inverse function for the following;

Y = aX + bX^c

Clearly it is not possible to find 'X' in terms of 'Y' so how does one approach the finding of the inverse function? I also have to find the integral to the inverse function but just cannot get past the first step using the examples already provided in the forum. Any helpful tips would be greatly appreciated.

Thanks!