restricted inverse

Practise restricted inverse with an original VectorPaths question, worked explanation and related VCE Methods practice.

1 practice marks

Original practice question

The function $f: D \to R$ with rule $f(x) = 3x^3 - 12x^2 + 12x$ will have an inverse function for

Worked explanation

• Find stationary points

  \[f'(x) = 9x^2 - 24x + 12 = 0 \implies x = \frac{2}{3} \text{ or } x = 2\]

• Determine monotonic intervals

  \[f \text{ is increasing on } [2, \infty)\]

E

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