Inverse Functions

[ladyluthien3]

Hi
I need help solving a problem.

f(x)=x+1/x-3

I need to find its inverse.

I'll be grateful of any help I can get.
btw the / means divieded by just in case you dont know.

 

[pka]

Solve this for y: \(\displaystyle \L x = \frac{{y + 1}}{{y - 3}}\)

 

[ladyluthien3]

yeah i know how to do that much but what happens afterwards?

f(x)=x+1/x-3
y=x+1/x-3
x=y+1/y-3

Now you have to solve for y but now there are two instead of one.

So now what do i do?

 

[stapel]

yeah i know how to do that much but what happens afterwards?

All you did was switch the variables. You still need to solve for "y=". :wink:

A good first step would be to multiply through, to get rid of the fraction. Then get all the x-terms together on one side of the "equals", with everything else on the other side. Factor out the x, and divide through. :idea:

Note: We're fairly sure of what you probably mean, but "x+1/x-3" is "x + (1/x) - 3", not "(x + 1)/(x - 3)". When you reply, please use grouping symbols to make your intended meaning clear. Thank you!

Eliz.