Algebra 4 summary

Key learning points

• Function notation $f(x)$ and composites $fg$.
• Find inverses when the function is one-to-one.
• Link algebra to graphs where helpful.
• Attempt structured working even if a later step is unclear.

Worked example 1 — Composite

If $f(x)=x+1$ and $g(x)=2x$, find $fg(3)$.

Working

Apply $g$ first: $g(3)=6$, then $f(6)=7$.

Worked example 2 — Function notation and composites

Use this method from the Algebra 4 sheet: Function notation $f(x)$ and composites $fg$.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Find inverses when the function is one-to-one

Use this method from the Algebra 4 sheet: Find inverses when the function is one-to-one.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Link algebra to graphs where helpful

Use this method from the Algebra 4 sheet: Link algebra to graphs where helpful.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — Attempt structured working even if a later step is uncl

Use this method from the Algebra 4 sheet: Attempt structured working even if a later step is unclear.

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.