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# Inverse Functions

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by

## Mr Mattock

on 31 October 2016

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#### Transcript of Inverse Functions

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.

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

Activities
Activity