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 $p(x) = 3x^2 + -2$ and $q(x) = x^2 + 1$. Find $p(q(1))$.

Worked explanation

• f(g(x)) = f evaluated at g(x)

  \[f(g(x)) = 3 \left(x^{2} + 1\right)^{2} - 2\]

• Simplify the result

  \[= 10\]

10

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