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

1 Answer
Konstantinos Michailidis
May 31, 2016

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

I rename "f(x)f(x)" as "yy" hence:

y=(2x-3)/(x+4)y=2x−3x+4

Then I solve for "xx" :

y*(x+4)=2x-3=>yx-2x=-3-4y=> x(y-2)=-3-4y=>x=(-3-4y)/(y-2)y⋅(x+4)=2x−3⇒yx−2x=−3−4y⇒x(y−2)=−3−4y⇒x=−3−4yy−2

Then I switch xx and yy:

y=(-3-4x)/(x-2)y=−3−4xx−2

And rename "yy" as "f-inverse" hence

f^-1(x)=(-3-4x)/(x-2)f−1(x)=−3−4xx−2

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

The inverse function is a function indeed.

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