Question

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)

Answer 1

ok this takes a bit of algebra

Answer 2

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

Answer 3

\[x=\frac{y+3}{y-2}\] multiply to get rid of the denominator
\[x(y-2)=y+3\] multiply out on the left
\[xy-2x=y+3\]

Answer 4

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
\[y=\frac{2x+3}{x-1}\]

Answer 5

and thats the inverse right?

Answer 6

that is it!

Answer 7

thanks!:)

Answer 8

i mean it is it when you write
\[f^{-1}=\frac{2x+3}{x-1}\]