function analysis

Practise function analysis with an original VectorPaths question, worked explanation and related VCE Methods practice.

1 practice marks

Original practice question

Let $q(x) = x^2 - 2mx + m + 6$ where $m$ is a real constant. If $q$ has an inverse function, what possible values can $m$ have?

Worked explanation

• Analyze invertibility

  \[q(x) = (x - m)^2 - m^2 + m + 6 \text{ is not one-to-one on } R\]

The function $q$ cannot have an inverse on $R$ for any value of $m$, since $q$ is a quadratic and not one-to-one on $R$.

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