Thread: The inverse of a function

Hi,

I would like some help with a problem.
Show that has an inverse and find



How do you invert fractions like this?

//Jones

Originally Posted by Jones

Hi,

I would like some help with a problem.
Show that has an inverse and find



How do you invert fractions like this?

//Jones

... domain is all reals.

for all x, telling us that f(x) is a strictly increasing function.

since f(x) is strictly increasing, it is 1-1 over its domain, and as such has an inverse function.


next, note that

that means that

Note, that this problem did NOT ask you to actually find the inverse function- and skeeter did not. However, since you asked:

Start by witing the function as
and swapping x and y:

Now solve for y:



Solve that cubic equation for y. That, of course, is the hard part and probably why the problem did not require you to find the inverse!

Oh dang, i thought you had to solve the darn thing