composite function evaluation

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

2 practice marks

Original practice question

Let $p(x) = -1x^2 + -1$ and $q(x) = x^2 + 2$. Find $p(q(2))$.

Worked explanation

• f(g(x)) = f evaluated at g(x)

  \[f(g(x)) = - \left(x^{2} + 2\right)^{2} - 1\]

• Simplify the result

  \[= -37\]

-37

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