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Q.
Let $f ( x )=\frac{2}{ x -3}, x \neq 3$ The inverse of $f ( x )$ is $g(x)=\frac{2+a x}{x}, x \neq 0 .$ Then $a$ =
Relations and Functions - Part 2
Solution:
Let $f(x)=y=\frac{2}{x-3}, x \neq 3$.
Then $x-3=\frac{2}{y}$ or
$x=\frac{2}{y}+3$ or
$x=\frac{2+3 y}{y}$
Replacing $x$ by $y$ and $y$ by $x$, we get:
$y=\frac{2+3 x}{x}$
Let $y = g ( x )=\frac{2+3 x }{ x }$,
then $g ( x )$ is the inverse of $f ( x )$.
Hence, $a =3$