Question

Find the inverse function..

Answer 1

write the function without the function notation\[y=\frac{2x-3}{x+5}\]exchange the positions of the domain and range variables\[x=\frac{2y-3}{y+5}\]solve for y\[xy+5x=2y-3\]\[5x+3=2y-xy\]\[5x+3=y(2-x)\]\[y=f ^{-1}(x)=\frac{5x+3}{2-x}\]

Answer 2

The domain of f is the same as the range of f-inverse\[(-\infty,5) \cup(5, \infty)\]

Answer 3

Thank you MANDOLINO!!!!

Answer 4

ur welcome :})

FYI: Here is the function and its inverse graphed; note they are symmetric about the line y=x; this is true of any function and its inverse

Answer 5

O wow thank you so much!