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Year 11
Higher

Solving equations involving functions

I can solve equations involving functions.

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New
New
Year 11
Higher

Solving equations involving functions

I can solve equations involving functions.

Download all resources
arrow-right
Share activities with pupils
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Lesson details

Key learning points

  1. A function may have a given output.
  2. 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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

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

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: $$x=-{1\over5}$$
$$x={1\over5}$$
$$x=2$$
$$x=5$$