Pure 1 course · All short practice · Notes & examples

Maths4U Original · 9709 Pure 1

Composite functions and their domains

Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.

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Recall · M4U-P1-QP-FUNCTIONS-COMPOSITE-01

composition order

Maths4U Original · Short practice

Let \(f(x)=2x+1\), \(g(x)=x^2\). Find \(f(g(3))\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Method · M4U-P1-QP-FUNCTIONS-COMPOSITE-02

composition noncommutativity

Maths4U Original · Short practice

With \(f(x)=2x+1\), \(g(x)=x^2\), find \(g(f(3))\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Apply · M4U-P1-QP-FUNCTIONS-COMPOSITE-03

composite domain

Maths4U Original · Short practice

Let \(f(x)=\sqrt{x}\), \(g(x)=x-4\). What is the real domain of \(f(g(x))\)?

Choose one answer.

Check understanding · M4U-P1-QP-FUNCTIONS-COMPOSITE-04

existence condition

Maths4U Original · Short practice

Let \(f:A\to B\) and \(g\) have domain \(C\). When can \(g\circ f\) use every input of \(f\)?

Choose one answer.

Syllabus follow-up · M4U-P1-QP-FUNCTIONS-COMPOSITE-05

range with unattained bound

Maths4U Original · Short practice

Let \(f(x)=1/x\), \(x\ge2\). What is its range?

Choose one answer.

Fresh review variant · M4U-P1-QP-VAR-FUNCTIONS-COMPOSITE-01

composition order

Maths4U Original · Short practice

For \(f(x)=3x-2\), \(g(x)=x^2\), find \(f(g(2))\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-FUNCTIONS-COMPOSITE-02

composition noncommutativity

Maths4U Original · Short practice

For \(f(x)=3x-2\), \(g(x)=x^2\), find \(g(f(2))\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-FUNCTIONS-COMPOSITE-03

composite domain

Maths4U Original · Short practice

For \(f(x)=\sqrt{x}\), \(g(x)=x-7\), enter the lower endpoint of the real domain of \(f(g(x))\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-FUNCTIONS-COMPOSITE-04

existence condition

Maths4U Original · Short practice

Let \(f(x)=2x\) on \([0,a]\), \(a>0\), and let g have domain \([0,10]\). Find the greatest a for which \(g\circ f\) is defined for every input of f.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-FUNCTIONS-COMPOSITE-05

range with unattained bound

Maths4U Original · Short practice

For \(f(x)=3/x\), \(x\ge2\), enter the upper endpoint of its range.

Enter one number or fraction. Round decimals to at least six decimal places when needed.