Inverse Functions: Warm-Up Quiz and Learning Objectives, Schemes and Mind Maps of Mathematics

A warm-up quiz on inverse functions, designed for high school students. It covers key concepts like finding the inverse of a function, understanding its effect, and solving related problems. The quiz includes exercises on finding the inverse of a function, working with composite functions, and applying the concept to real-world scenarios like finding the upper bound of a triangle's area. The document also outlines learning objectives, providing a clear understanding of the expected knowledge and skills.

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2024/2025

Uploaded on 02/13/2025

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13 February 2025
Warm-Up Quiz
Inverse Functions
Do Next:
1MWB: Show that  fg(x) = 2x2 + 16x + 35
2Here is a number machine.
(a)  Work out the output when the input is 5
(b)  Work out the input when the output is 19
3Find gf(x)
4Solve  fg(x) = gf(x)
5Two sides of a triangle are measured to 1 decimal place.
The angle between the sides is measured to the nearest degree.
Find the Upper Bound of 7.2
Find the Upper Bound of 13.6
6Work out the upper bound for the area of the triangle.
You must show your working.
For all values of x, 
 f(x) = 2x2 + 3  g(x) = x + 4
(2x2 + 7)
–1.75
= 9
= 10
= 7.25
= 13.65
x= 400 to 1 significant figure.
y= 25 to 2 significant figures.
Work out the maximumintegervalue of
= 18
46.6(4…)
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13 February 2025

Warm-Up Quiz

Inverse Functions

Do Next:

1 MWB:^ Show that^ fg( x ) =^ 2x

2

  • 16 x + 35

2 Here is a number machine.

(a) Work out the output when the input is 5 (b) Work out the input when the output is 19

3 Find^ gf( x )

4 Solve^ fg( x ) = gf( x )

5 Two sides of a triangle are measured to 1 decimal place.

The angle between the sides is measured to the nearest degree. Find the Upper Bound of 7. Find the Upper Bound of 13.

6 Work out the upper bound for the area of the triangle.

You must show your working.

For all values of x ,

f( x ) = 2 x^2 + 3 g( x ) = x + 4

(2 x

2

x = 400 to 1 significant figure.

y = 25 to 2 significant figures.

Work out the maximum integer value of

Learning Objectives

To know

- What an inverse function does

- How to find the inverse of a function

How to answer exam questions on

inverse functions

New Learning

An inverse function , , is a function which reverses the effect of.

How do we reverse the effect of this?

I Do

Find

We Do

Find

Check for Understanding

Find

CfU

Find

More Independent Practice

More Independent Practice

More Independent Practice

More Independent Practice