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 $g(x) = 2x^2 + -1$ and $h(x) = x^2 + -1$. Find $g(h(3))$.

Worked explanation

• f(g(x)) = f evaluated at g(x)

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

• Simplify the result

  \[= 127\]

127

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