Thread: Find the Inverse?

Hello, I've been trying to figure out how to solve this function but I keep getting stuck. The question asks:

Find a formula for the inverse of the function:

y = e^x / 1+5e^x

My teacher said to substitute the variable p to replace e^x to make the function easier to solve.

y = p / 1+5p^2

I'm not really sure how to go about solving this question. Would I multiply all sides by the denominator to get rid of it and then somehow solve from there?

Help is appreciated, so thanks in advance.

Originally Posted by dark-ryder341

y = e^x / 1+5e^x

My teacher said to substitute the variable p to replace e^x to make the function easier to solve.

y = p / 1+5p^2

How did you arrive at ?


What is the original function?



or

Oops, my mistake. I meant to write y = p / 1+5p

The p is just a substitution for e^x

The original function is:



Thanks.

Originally Posted by dark-ryder341

Oops, my mistake. I meant to write y = p / 1+5p

The p is just a substitution for e^x

The original function is:



Thanks.

The inverse is given by where .

Your job is to make y the subject. Let :



.

Substitute back for p and solve for y.

Thanks so much. It makes a lot of sense now.

So now, substituting e^y back in, I get

e^y = x / 1-5x

If I take the ln of both sides:

lne^y = ln (x/1-5x)

lne^y = y...therefore

y = ln (x/1-5x)