Inverse functions and restricted domains · Short practice

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Recall

Inverse functions and restricted quadratics — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = \left(x - 16\right)^{2} + 2\) for \(\displaystyle x\ge 16\). Here \(\displaystyle a=1, h=16, k=2, d=5\).

Find the least output of f.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Inverse functions and restricted quadratics — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 \left(x - 17\right)^{2} + 3\) for \(\displaystyle x\ge 17\). Here \(\displaystyle a=2, h=17, k=3, d=2\).

Find the least output of f.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Inverse functions and restricted quadratics — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 \left(x - 17\right)^{2} + 3\) for \(\displaystyle x\ge 17\). Here \(\displaystyle a=2, h=17, k=3, d=2\).

Find \(\displaystyle f^{−1}\) at the output \(\displaystyle k+a d^{2}\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Inverse functions and restricted quadratics — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 \left(x - 18\right)^{2} + 4\) for \(\displaystyle x\ge 18\). Here \(\displaystyle a=3, h=18, k=4, d=3\).

Find \(\displaystyle f^{−1}\) at the output \(\displaystyle k+a d^{2}\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Inverse functions and restricted quadratics — objective 3

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 \left(x - 18\right)^{2} + 4\) for \(\displaystyle x\ge 18\). Here \(\displaystyle a=3, h=18, k=4, d=3\).

Find the input whose output is \(\displaystyle k+4a d^{2}\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Inverse functions and restricted quadratics — objective 3

Maths4U Original · Short practice

\(f{\left(x \right)} = \left(x - 19\right)^{2} + 5\) for \(\displaystyle x\ge 19\). Here \(\displaystyle a=1, h=19, k=5, d=4\).

Find the input whose output is \(\displaystyle k+4a d^{2}\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Inverse functions and restricted quadratics — objective 4

Maths4U Original · Short practice

\(f{\left(x \right)} = \left(x - 19\right)^{2} + 5\) for \(\displaystyle x\ge 19\). Here \(\displaystyle a=1, h=19, k=5, d=4\).

Find the lower endpoint of the domain of f.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Inverse functions and restricted quadratics — objective 4

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 \left(x - 20\right)^{2} + 6\) for \(\displaystyle x\ge 20\). Here \(\displaystyle a=2, h=20, k=6, d=5\).

Find the lower endpoint of the domain of f.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

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