Question

If $f(x)=\frac{2 x-1}{x+5}, x \neq-5$, then $f^{-1}(x)$ is equal to

• A. $\frac{x+5}{2 x-1}, x \neq \frac{1}{2}$
• B. $\frac{5 x+1}{2-x}, x \neq 2$
• C. $\frac{x-3}{2 x+1}, x \neq \frac{1}{2}$
• D. $\frac{5 x-1}{2-x}, x \neq 2$

Answer 1

Answer: (D)

Let $y=\frac{2 x-1}{x+5}$
$ \Rightarrow x=\frac{5 y+1}{2-y}$
$ \therefore f^{-1}(x)=\frac{5 x-1}{2-x}, x \neq 2$