Math on the Mind

45

)122()83(

)(

x

xx

xgxfxgf

g - f and g f Find

.122g and 83fLet

xxxx

20

)122()83(

)(

x

xx

xgxfxgf

Composition of Functions

Unit 3Lesson 7

Composite Function

The composition of function g with function is written as xfgxfg

1

2

1. Evaluate the inner function f(x) first.

2. Then use your answer as the input of the outer function g(x).

The composition (f o g)(x) or f(g(x)) is read “f of g of x.”

Reading Math

Step 1: Find g(3)

Given f(x) = 2x – 3 and g(x) = x2, find f(g(3))

g(3) = 32

Step 2: Find f(9) = 9

f(9) = 2(9) – 3= 15

So f(g(3)) = 15.

Step 1 Find f(3)

Given f(x) = 2x – 3 and g(x) = x2, find g(f(3))

f(3) = 2(3) – 3

Step 2 Find g(3) = 3

g(3) = 32

= 9So g(f(3)) = 9.

Suppose that and . Find

2( ) 1f x x ( ) 3g x x (2) ?g f

(2) 2g f g f2(2 1)g

(3)g

(3)(3) 9

Example

5 Find . and 2xfLet 2 fgxxgx

xfgxfg

)25(5 gfg

49)7( 2

)7(g

Example: 2 Find .7 and xfLet 23 fgxxgx

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