Question

Let $f(x)=\frac{2}{x-3},x\ne 3$ The inverse of $f(x)$ is $g(x)=\frac{2+ax}{x},x\ne 0.$ Then $a$ =

• A. 5
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

Let $f(x)=y=\frac{2}{x-3},x\ne 3$.
Then $x-3=\frac{2}{y}$ or
$x=\frac{2}{y}+3$ or
$x=\frac{2+3y}{y}$
Replacing $x$ by $y$ and $y$ by $x$, we get:
$y=\frac{2+3x}{x}$
Let $y=g(x)=\frac{2+3x}{x}$,
then $g(x)$ is the inverse of $f(x)$.
Hence, $a=3$