Correct Answer: Option D

Explanation

\(f :x→\frac{x + 2}{x - 3},x ≠ 3, f = ?\)

Let \(f :x=y\)

\(y=\frac{x + 2}{x - 3}\)

\(=x+2=y(x-3)\)

\(=x-xy=-3y-2\)

\(=x(1-y)=-3y-2\)

\(=x=\frac{-3y - 2}{1 - y}=\frac{-(3y + 2)}{- (y - 1)}\)

\(=x=\frac{3y + 2}{y - 1}\)

\(∴f ^{-1} : x=\frac{3x + 2}{x - 1},x ≠ 1\)

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