existence condition

Practise existence condition with an original VectorPaths question, worked explanation and related VCE Methods practice.

2 practice marks

Original practice question

Let $h(x) = x^2 - 6x + 5$, where $x \in R$. Find the largest value of $b$ such that when $h$ is restricted to the interval $(-\infty, b]$, the restricted function has an inverse.

Worked explanation

• Find the vertex

  \[h(x) = (x-3)^2 - 4, \quad \text{vertex at } x = 3\]

• Determine largest b

  \[b = 3\]

$b = 3$

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