Given $f(x)=\dfrac5x+\dfrac{13}2$ , find an expression for $f^{-1}(x)$ .

Model answer

10/(2x-13)

Also accepted: f^-1(x)=10/(2x-13)

Explanation:

y=\dfrac5x+\dfrac{13}2\Rightarrow x=\dfrac{10}{2y-13}

, so

f^{-1}(x)=\dfrac{10}{2x-13}

Derived from ZIMSEC Pure Mathematics Paper 2, November 2025, Q5

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