Composition and an input constraint

Practise composition and an input constraint with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=2x+1$ and $g(x)=x^2$, both with domain $\mathbb R$. (a) Find and expand $g(f(x))$. [2 marks] (b) Find all x such that $g(f(x))=9$. [2 marks]

Worked explanation

• Part (a)

  Substitute the whole expression for f into g: $g(f(x))=(2x+1)^2=4x^2+4x+1$.

• Part (b)

  $(2x+1)^2=9$ gives $2x+1=\pm3$, hence $x=1$ or $x=-2$.

(a) $4 x^{2} + 4 x + 1$.; (b) $x=-2,1$.

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