Maths Extension 1 Year 11 - Module 1 - Lesson 8

Composite Functions

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

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Date
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1. Lesson focus

Composite functions. For f∘g, evaluate g first and substitute its entire output into f; order generally matters.

Success criteria

  • Apply the lesson method accurately in a routine example.
  • Show each algebraic or domain step and check the result.
  • Explain why the method and restrictions fit the question.

2. Worked practice

1. Let f(x)=x²+1 and g(x)=2x−3. Find (f∘g)(x).

2. For the same functions, find (g∘f)(x).

3. Find (f∘g)(2) and (g∘f)(2).

3. Challenge

Let f(x)=√x and g(x)=x−4. State the domain of (f∘g)(x).

4. Multiple choice

For f∘g, which function is applied first?

A. both at once

B. f

C. g

D. neither

Worked answer key

Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.

1. Let f(x)=x²+1 and g(x)=2x−3. Find (f∘g)(x).

f(g(x))=(2x−3)²+1=4x²−12x+10.

2. For the same functions, find (g∘f)(x).

g(f(x))=2(x²+1)−3=2x²−1.

3. Find (f∘g)(2) and (g∘f)(2).

g(2)=1, f(1)=2; f(2)=5, g(5)=7. The values are 2 and 7.

Challenge. Let f(x)=√x and g(x)=x−4. State the domain of (f∘g)(x).

√(x−4) requires x−4≥0, so x≥4.

Multiple choice. For f∘g, which function is applied first?

Correct answer: C. In f(g(x)), evaluate the inner function g before applying the outer function f.

HSCScience - Printable lesson worksheet - Maths Extension 1 Year 11 - Module 1 - Lesson 8

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