Answer
one-to-one. $f^{-1}(x)=\frac{4x}{x+1}, x\ne-1$
Work Step by Step
Step 1. Graph $f(x)=\frac{-x}{x-4}, x\ne4$ as shown in the figure.
Step 2. The function is one-to-one. $y=\frac{-x}{x-4}\longrightarrow x=\frac{4y}{y+1}\longrightarrow f^{-1}(x)=\frac{4x}{x+1}, x\ne-1$
