Functions

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.

Multiple Choice

Starter:

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

• 13

• 10

• 12

• 11

Multiple Choice

Starter:

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

• 9

• 10

• 8

• 12

Multiple Choice

Starter:

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

• 8

• 5

• 7

• 9

Multiple Choice

Starter:

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

• 7

• 4

• 6

• 5

Multiple Choice

Starter:

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

• -10

• -12

• 12

• 8

Multiple Choice

Starter:

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

• 8

• 3

• 2

• 5

Multiple Choice

Starter:

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

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

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

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

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

Examples:

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

Examples : Composite functions