WAEC Further Mathematics 2024 Paper

Concept:The inverse of a function is found by solving for $x$ in terms of $y$, then swapping $x$ and $y$.Explanation:Let $y = f(x) = \frac{2 - x}{x}$, where $x \neq 0$.Multiply both sides by $x$ to remove the denominator:$xy = 2 - x$.Bring the $x$-terms together on one side:$xy + x = 2$.Factor out $x$:$x(y + 1) = 2$.Divide both sides by $(y + 1)$, provided $y \neq -1$:$x = \frac{2}{y + 1}$.Now interchange $x$ and $y$ to write the inverse function:$f^{-1}(x) = \frac{2}{x + 1}$, with $x \neq -1$.The original domain $x \neq 0$ gives a range $y \neq -1$, so the excluded value for the inverse is correct.Answer:Option B: $f^{-1}(x) = \frac{2}{x + 1}$, $x \neq -1$.