Pure 1 course · All short practice · Notes & examples

Maths4U Original · 9709 Pure 1

Inverse functions, domain and range

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-INVERSE-01

inverse evaluation

Maths4U Original · Short practice

Let \(f(x)=4x-7\). Find \(f^{-1}(9)\).

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

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

inverse versus reciprocal

Maths4U Original · Short practice

Find the inverse of \(f(x)=3-2x\).

Choose one answer.

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

rational inverse

Maths4U Original · Short practice

Let \(g(x)=\frac{x+1}{x-2}\), \(x\ne2\). Find \(g^{-1}(3)\).

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

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

one-to-one

Maths4U Original · Short practice

Which function is one-to-one on the whole real line?

Choose one answer.

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

inverse evaluation

Maths4U Original · Short practice

For \(f(x)=3x-4\), find \(f^{-1}(11)\).

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

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

inverse versus reciprocal

Maths4U Original · Short practice

For \(f(x)=7-3x\), find \(f^{-1}(1)\).

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

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

rational inverse

Maths4U Original · Short practice

For \(g(x)=(x+2)/(x-1)\), find \(g^{-1}(4)\).

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

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

one-to-one

Maths4U Original · Short practice

How many real inputs of \(h(x)=x^2\) give output 25?

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