Inverse of a reciprocal function

Practise inverse of a reciprocal function with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=4/(x-1)+2$, with $x\ne1$. (a) Find the inverse rule. [2 marks] (b) State the domain and range of the inverse. [2 marks]

Worked explanation

• Part (a)

  $y-2=4/(x-1)$ implies $x-1=4/(y-2)$. Rearrange and exchange variables.

• Part (b)

  The original output can never be 2 and the original input can never be 1. Inversion exchanges these restrictions.

(a) $f^{-1}(x)=1+4/(x-2)$.; (b) Domain $\mathbb R\setminus\{2\}$; range $\mathbb R\setminus\{1\}$.

Original VectorPaths practice; not an official VCAA question or marking rubric.