x 3 2 1 0 1 2 3 fx 11 9 7 5 3 1 1 gx 8 3 0 1 0 3 8 Evaluate

x

-3

-2

-1

0

1

2

3

f(x)

11

9

7

5

3

1

-1

g(x)

-8

-3

0

1

0

-3

-8

Evaluate each using the table (Show your work):

i.(f o g)(1)

ii.(g o f)(2)

iii.(g o g)(1)

iv.(f o g)(2)

v.(g o f)(3)

vi.(f o f)(3)

x	-3	-2	-1	0	1	2	3
f(x)	11	9	7	5	3	1	-1
g(x)	-8	-3	0	1	0	-3	-8

Solution

We know that

(f o g)(x) = f ( g(x) )

(g o f)(x) = g ( f(x) )

1 )   (f o g)(1) = f ( g(1) )

= f ( 0 )  

= 5

2 )   (g o f)(2) = g ( f(2) )

= g ( 1 )

= 0

3 ) (g o g)(1) =  g ( g(1) )

= g ( 0 )

= 1

4 )   (f o g)(2) =  f ( g(2) )

= f ( -3 )

= 11

5 ) (g o f)(3) = g ( f(3) )

= g ( -1 )

= 0

6 ) (f o f)(3) =   f ( f(3) )

= f ( -1 )

= 7