How do i solve this? after setting the function equal to y, how do i solve it for x? do i solve for x and then interchange with y?

First, realize that the inverse f⁻¹ means switch x and y
so what you do is switch x and y and solve for y
so
y=f(x)

y=(x+2)/(x-3)
switch
x=(y+2)/(y-3)
times both sides by (y-3)
x(y-3)=y+2
expand
xy-3x=y+2
minus xy both sides
-3x=y-xy+2
minus 2 both sides
-3x-2=y-xy
undistribute y
-3x-2=y(1-x)
divide both sides by (1-x)



now show that f(f⁻¹(x))=x