Starter: f ( x ) = 4 x − 9 F i n d t h e i n v e r s e f u n c t i o n . f\left(x\right)=4x-9\ \ \ Find\ the\ inverse\ function. f ( x ) = 4 x − 9 F i n d t h e i n v e r s e f u n c t i o n .

f − 1 ( x ) = x + 9 4 f^{-1}\left(x\right)=\frac{x+9}{4} f − 1 ( x ) = 4 x + 9

f − 1 ( x ) = x − 9 4 f^{-1}\left(x\right)=\frac{x-9}{4} f − 1 ( x ) = 4 x − 9

f − 1 ( x ) = x + 9 4 f^{-1}\left(x\right)=\frac{x+9}{4} f − 1 ( x ) = 4 x + 9

f − 1 ( x ) = x − 4 5 f^{-1}\left(x\right)=\frac{x-4}{5} f − 1 ( x ) = 5 x − 4

Functions Lesson Slides: 6 Slides

6 Slides • 7 Questions

1

Functions

Learning Objectives:

Be able to understand function notation and to work out the input and output of a function

Be able to find the inverse of a function

Be able to find the composite of a function.

2

Multiple Choice

Starter:

f\left(x\right)=3x-5\ Find\ the\ value\ of\ f\left(6\right)

1

13

2

10

3

12

4

11

3

Multiple Choice

Starter:

f\left(x\right)\ =\ x^2-\frac{10}{x}\ \ \ Find\ the\ value\ of\ \left(-2\right)

1

9

2

10

3

8

4

12

4

Multiple Choice

Starter:

$f\left(x\right)=\frac{3x+2}{x}\ \ Find\ the\ value\ of\ \left(0.5\right)$

1

8

2

5

3

7

4

9

5

Multiple Choice

Starter:

f\left(x\right)=2x-7\ \ f\left(a\right)=3\ Find\ the\ value\ of\ a\ .

1

7

2

4

3

6

4

5

6

Multiple Choice

Starter:

$f\left(x\right)=\frac{1}{2}x+4\ \ \ f\left(a\right)=-2\ \ Find\ the\ value\ of\ a.$

1

-10

2

-12

3

12

4

8

7

Multiple Choice

Starter:

$f\left(x\right)=\frac{x}{x-1}\ \ \ f\left(x\right)=2\ Find\ the\ value\ of\ x.$

1

8

2

3

2

4

5

8

Multiple Choice

Starter:

$f\left(x\right)=4x-9\ \ \ Find\ the\ inverse\ function.$

1

$f^{-1}\left(x\right)=\frac{x-9}{4}$

2

$f^{-1}\left(x\right)=\frac{x+9}{4}$

3

$f^{-1}\left(x\right)=\frac{x+9}{4}$

4

$f^{-1}\left(x\right)=\frac{x-4}{5}$

9

Examples:

How to find the inverse of a function using the algebraic method

10

11

Examples : Composite functions

12

13

Functions

Learning Objectives:

Be able to understand function notation and to work out the input and output of a function

Be able to find the inverse of a function

Be able to find the composite of a function.

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