Question

How do you find the inverse of `f(x) = (2x-3)/(x+4)` and is it a function?

Answer 1

The original function is defined in `D_f=R-{-4}`.

I rename "`f(x)`" as "`y`" hence:

`y=(2x-3)/(x+4)`

Then I solve for "`x`" :

#y*(x+4)=2x-3=>yx-2x=-3-4y=> x(y-2)=-3-4y=>x=(-3-4y)/(y-2)#

Then I switch `x` and `y`:

`y=(-3-4x)/(x-2)`

And rename "`y`" as "f-inverse" hence

`f^-1(x)=(-3-4x)/(x-2)`

which is defined for `D_(f^-1)=R-{2}`

The inverse function is a function indeed.