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

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Answer 1 · 2016-05-31T12:58:45

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.