**Inverse Functions**

Starter

A function machine works as follows:

Main Activity 1

Complete the inverse functions worksheet

Inverse Functions

f(x) = 4x - 5. Find f (x).

g:x 2x + 5. Find g :x

x 2

+ 5

Find the

input

when the

output

is...

(a) 11

(b) 25

(c) 3

(d) 6

Starter

A function machine works as follows:

x 2

+ 5

Find the

input

when the

output

is...

(a) 11

3

(b) 25

10

(c) 3

-1

(d) 6

1

2

-1

-1

2

Inverse Functions

f(x) = 4x - 5. Find f (x).

-1

-1

2

x4

-5

+5

/4

x

x + 5

x + 5

4

f (x) = x + 5

4

-1

2

x2

+5

-5

/2

x

x - 5

x - 5

2

x - 5

2

f (x) = x - 5

-1

2

g:x 2x + 5. Find g :x

**L.O. - Understand what the inverse**

of a function is, and find inverse functions.

of a function is, and find inverse functions.

Inverse Functions

f(x) = 5 - 4x. Find f (x).

g:x 8 . Find g :x

-1

-1

2x + 3

Inverse Functions

f(x) = 5 - 4x. Find f (x).

g:x 8 . Find g :x

-1

-1

2x + 3

x -4 + 5

/-4 - 5

x

x - 5

x - 5

-4

f (x) = 5 - x

4

-1

x2 +3 reciprocal x8

/2 -3 reciprocal /8

x

x

8

8

x

8

x

-3

8

x

-3

2

Main Activity 1

(a) x - 3 (b) x - 9 (c) 5 - x (d) 4x - 3 (e) 3x + 5 (f) (8 - x)

10 2 6 2

5

3

(a) x + 4 (b) x (c) 1 (d) 1 (e) 1

3 x x - 2 x

+ 5

4

(a) (x - 2) (b) 3x + 4 (c) -5x - 1 (d) 1 (e) 4

2 10x x

-3

(a) x+6 -3 (b) x-1 + 2 (c) x+8.25 -2.5 (d) x-2.75 +1.5

(e) 9-x -1 (f) 20-x + 2

5

Dice of Ultimate Power

1) Give a key word for the lesson.

2) Summarise one key point for the

lesson.

3) Explain one thing you have learned this

lesson.

4) State one thing you still don't understand following this lesson.

5) Suggest one thing you would like to find out

based on this lesson.

6) Free choice from 1 to 5, or another you make

up.

Key Notes

Inverse of reciprocal = reciprocal.

Treat 6 - 7x as -7x + 6 (i.e. multiply

by - 7 then add 6)

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

Answers

**Worked**

Example

Example

**Worked**

Example

Example