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)

Question

anonymous · Answer

ok this takes a bit of algebra

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

and thats the inverse right?

anonymous · Answer

that is it!

anonymous · Answer

thanks!:)

anonymous · Answer

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