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Solving equations involving functions

I can solve equations involving functions.

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Lesson 5 of 14

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Year 11

Solving equations involving functions

I can solve equations involving functions.

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Lesson details

Key learning points

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

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.

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.

Pupils need to be able to manipulate equations in order to access this lesson. Consider reviewing these skills before this lesson if you think your pupils would benefit from this.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
An equation is used to show two expressions that are __________ each other.

unlike

Correct answer: equal to

unequal to

Q2.
If $${\text{f}}(x)=7x−4$$ evaluate $${\text{f}}(8)$$.

Correct Answer: 52, f(8)=52

Q3.
Solve $$7x-5=-26$$ $$x=$$

Correct Answer: -3, x=-3

Q4.
Solve $$7x-5=31-3x$$ $$x=$$

Correct Answer: 3.6, x=3.6

Q5.
Solve $$x^2+3x-26=7x-5$$.

Correct answer: $$x=7$$

$$x=3$$

Correct answer: $$x=-3$$

$$x=-7$$

This equation has no solutions.

Q6.
Solve $${4\over{3x+7}}={3\over{x-1}}$$ $$x=$$

Correct Answer: -5, x=-5

Assessment exit quiz

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6 Questions

Q1.
If $${\text{f}}(8)=145$$ then $${\text{f}}(x)$$ is a function which __________ $$8$$ to $$145$$.

multiplies

scales up

sums

Correct answer: maps

Q2.
If $${\text{f}}(x)=5(x−11)$$ solve $${\text{f}}(x)=50$$ $$x=$$ .

Correct Answer: 21, x=21

Q3.
If $${\text{f}}(x)=x^2−8x$$ solve $${\text{f}}(x)=-12$$.

Correct answer: $$x=6$$

Correct answer: $$x=2$$

$$x=-2$$

$$x=-6$$

This equation has no solutions.

Q4.
If $${\text{f}}(x)=5(x−11)$$ and $${\text{g}}(x)=2x+5$$ solve $${\text{f}}(x)={\text{g}}(x)$$ $$x=$$ .

Correct Answer: 20, x=20

Q5.
If $${\text{f}}(x)={7\over{3x}}$$ solve $${\text{f}}(x)=21$$.

$$x=9$$

$$x=3$$

$$x=1$$

$$x={1\over3}$$

Correct answer: $$x={1\over9}$$

Q6.
If $${\text{f}}(x)={{5x+11}\over{2}}$$ and $${\text{g}}(x)=-{{1}\over{x}}$$ solve $${\text{f}}(x)={\text{g}}(x)$$.

Correct answer: $$x=-2$$

Correct answer: $$x=-{1\over5}$$

$$x={1\over5}$$

$$x=2$$

$$x=5$$

Lesson appears in

UnitMaths / Functions and proof

Maths

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Solving equations involving functions

Solving equations involving functions

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.An equation is used to show two expressions that are __________ each other.

Q2.If $${\text{f}}(x)=7x−4$$ evaluate $${\text{f}}(8)$$.

Q3.Solve $$7x-5=-26$$ $$x=$$

Q4.Solve $$7x-5=31-3x$$ $$x=$$

Q5.Solve $$x^2+3x-26=7x-5$$.

Q6.Solve $${4\over{3x+7}}={3\over{x-1}}$$ $$x=$$

Assessment exit quiz

6 Questions

Q1.If $${\text{f}}(8)=145$$ then $${\text{f}}(x)$$ is a function which __________ $$8$$ to $$145$$.

Q2.If $${\text{f}}(x)=5(x−11)$$ solve $${\text{f}}(x)=50$$ $$x=$$ .

Q3.If $${\text{f}}(x)=x^2−8x$$ solve $${\text{f}}(x)=-12$$.

Q4.If $${\text{f}}(x)=5(x−11)$$ and $${\text{g}}(x)=2x+5$$ solve $${\text{f}}(x)={\text{g}}(x)$$ $$x=$$ .

Q5.If $${\text{f}}(x)={7\over{3x}}$$ solve $${\text{f}}(x)=21$$.

Q6.If $${\text{f}}(x)={{5x+11}\over{2}}$$ and $${\text{g}}(x)=-{{1}\over{x}}$$ solve $${\text{f}}(x)={\text{g}}(x)$$.

Lesson appears in

UnitMaths / Functions and proof

Maths

Q1.
An equation is used to show two expressions that are __________ each other.

Q2.
If $${\text{f}}(x)=7x−4$$ evaluate $${\text{f}}(8)$$.

Q3.
Solve $$7x-5=-26$$ $$x=$$

Q4.
Solve $$7x-5=31-3x$$ $$x=$$

Q5.
Solve $$x^2+3x-26=7x-5$$.

Q6.
Solve $${4\over{3x+7}}={3\over{x-1}}$$ $$x=$$

Q1.
If $${\text{f}}(8)=145$$ then $${\text{f}}(x)$$ is a function which __________ $$8$$ to $$145$$.

Q2.
If $${\text{f}}(x)=5(x−11)$$ solve $${\text{f}}(x)=50$$ $$x=$$ .

Q3.
If $${\text{f}}(x)=x^2−8x$$ solve $${\text{f}}(x)=-12$$.

Q4.
If $${\text{f}}(x)=5(x−11)$$ and $${\text{g}}(x)=2x+5$$ solve $${\text{f}}(x)={\text{g}}(x)$$ $$x=$$ .

Q5.
If $${\text{f}}(x)={7\over{3x}}$$ solve $${\text{f}}(x)=21$$.

Q6.
If $${\text{f}}(x)={{5x+11}\over{2}}$$ and $${\text{g}}(x)=-{{1}\over{x}}$$ solve $${\text{f}}(x)={\text{g}}(x)$$.