Answer
one-to-one, $ f^{-1}(x)=\frac{-3x-5}{x-1}, x\ne1$
Work Step by Step
Step 1. Graph $f(x)=\frac{x-5}{x+3}, x\ne-3$ as shown in the figure.
Step 2. The function is one-to-one. $y=\frac{x-5}{x+3}\longrightarrow x=\frac{-3y-5}{y-1}\longrightarrow f^{-1}(x)=\frac{-3x-5}{x-1}, x\ne1$
