## animalsavior94 4 years ago 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)

1. anonymous

ok this takes a bit of algebra

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. animalsavior94

and thats the inverse right?

6. anonymous

that is it!

7. animalsavior94

thanks!:)

8. anonymous

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