WAEC 2023 · Paper 1 · Q11

Functions

A function $f$ is defined by $f: x \rightarrow \dfrac{x + 2}{x - 3}$ , $x \neq 3$ . Find the inverse of $f$ .

Worked solution (try it first)

Let $y = \dfrac{x + 2}{x - 3}$ and multiply up: $xy - 3y = x + 2$ .
Collect the $x$ terms on one side: $xy - x = 3y + 2$ , so $x(y - 1) = 3y + 2$ .
Divide by $y - 1$ : $x = \dfrac{3y + 2}{y - 1}$ .
So $f^{-1}(x) = \dfrac{3x + 2}{x - 1}$ , $x \neq 1$ , option B.

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