Question

find the inverse of the function defined by f (x) = x+5/x-2

Answer 1

\[y=\frac{x+5}{x-2}\]
Switching variable
\[x=\frac{y+5}{y-2}\]

\[x(y-2)=y+5\]

\[xy-2x=y+5\]
\[xy-y=5+2x\]
\[y(x-1)=5+2x\]
\[y=\frac{5+2x}{(x-1)}\]