Solving equations involving functions | Maths | Quizalize & Oak National Academy

Starter quiz

An equation is used to show two expressions that are __________ each other.

unlike

like

equal to ✓

unequal to
If ${\text{f}}(x)=7x−4$ evaluate ${\text{f}}(8)$ .

'52' ✓
Solve $7x-5=-26$ $x=$ ______

'-3' ✓
Solve $7x-5=31-3x$ $x=$ ______

'3.6' ✓
Solve $x^2+3x-26=7x-5$ .

$x=7$ ✓

$x=3$

$x=-3$ ✓

$x=-7$

This equation has no solutions.
Solve ${4\over{3x+7}}={3\over{x-1}}$ $x=$ ______

'-5' ✓

Exit quiz

If ${\text{f}}(8)=145$ then ${\text{f}}(x)$ is a function which __________ $8$ to $145$ .

multiplies

scales up

sums

maps ✓
If ${\text{f}}(x)=5(x−11)$ solve ${\text{f}}(x)=50$ $x=$ ______.

'21' ✓
If ${\text{f}}(x)=x^2−8x$ solve ${\text{f}}(x)=-12$ .

$x=6$ ✓

$x=2$ ✓

$x=-2$

$x=-6$

This equation has no solutions.
If ${\text{f}}(x)=5(x−11)$ and ${\text{g}}(x)=2x+5$ solve ${\text{f}}(x)={\text{g}}(x)$ $x=$ ______.

'20' ✓
If ${\text{f}}(x)={7\over{3x}}$ solve ${\text{f}}(x)=21$ .

$x=9$

$x=3$

$x=1$

$x={1\over3}$

$x={1\over9}$ ✓
If ${\text{f}}(x)={{5x+11}\over{2}}$ and ${\text{g}}(x)=-{{1}\over{x}}$ solve ${\text{f}}(x)={\text{g}}(x)$ .

$x=-2$ ✓

$x=-{1\over5}$ ✓

$x={1\over5}$

$x=2$

$x=5$

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

A function may have a given output.
It is possible to solve to find the input.

Common misconception

Small slips in working can lead to the wrong answer and pupils are not clear on how to check their working.

The lesson models how to check working so that the correct answer can be verified. This is good practice and helps pupils identify if there is an error.

Keywords

Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
Equation - An equation is used to show two expressions that are equal to each other.