Paper 1 · functions / inverse functions

Find the inverse of $f(x) = ax + b$ , where $a \ne 0$ and $b$ are constants.

f^{-1}(x) = \dfrac{1}{ax + b}

f^{-1}(x) = ax - b

f^{-1}(x) = \dfrac{x + b}{a}

f^{-1}(x) = \dfrac{x - b}{a}

Explanation: Setting

y=ax+b

gives

x=\tfrac{y-b}{a}

, so

f^{-1}(x)=\tfrac{x-b}{a}

Derived from ZIMSEC Mathematics Paper 1, June 2016, Q1

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