# Thread: We're homeschoolers stuck on derivatives of an inverse function.

1. ## We're homeschoolers stuck on derivatives of an inverse function.

We've used the Saxon text and don't understand its explanation. We've also look at the Princeton AP test book and still don't understand the explanation.

we don't understand how the given x and y values switch.

2. ## Re: We're homeschoolers stuck on derivatives of an inverse function.

I have no idea what your textbooks say, so I'll say it in my own way.

Suppose you have a function f which is continuous, one-to-one, and onto on a fixed interval [a,b] and you want to find its inverse. The inverse is defined to be a function g(x) such that g(f(x)) = x.

If we let f(x) = y that means that g(y) = x. Hence f(g(y)) = f(x) = y. so by the above definition f(x) and g(x) are inverse functions of one another.

f(x) sends x -> y
g(y) sends y -> x

the conditions one to one and onto guarantee unique images and pre-images. continuity is for simplicity. not needed, but if a function is discontinous you would express it as a split function and find an inverse for each segment.

3. ## Re: We're homeschoolers stuck on derivatives of an inverse function.

Hi,

A picture is worth a thousand words, so I hope the following drawing helps: