Here's the question you clicked on:
animalsavior94
determine if the function has an inverse that is a function. justify your answer. if it does, find the inverse function: f(x)=(x+3)/(x-2)
ok this takes a bit of algebra
rewrite as \[y=\frac{x+3}{x-2}\] and then either solve for x or switch x and y and solve for y. i will do it the second way
\[x=\frac{y+3}{y-2}\] multiply to get rid of the denominator \[x(y-2)=y+3\] multiply out on the left \[xy-2x=y+3\]
put all the y's on one side \[xy-y=2x+3\] factor out the y \[y(x-1)=2x+3\] divide to get y by itself \[y=\frac{2x+3}{x-1}\]
and thats the inverse right?
i mean it is it when you write \[f^{-1}=\frac{2x+3}{x-1}\]