Question

x | f(x) | g(x)
0 | 5 | 3
1 | 4 | 5
2 | 1 | 8
3 | 3 | 7
4 | 2 | 2
5 | 7 | 6
6 | 8 | 9
7 | 9 | 0
8 | 0 | 4
9 | 6 | 1

f(g(8)) =

g(f(6)) =

f(f(1)) =

g(g(9)) =

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Explanation:

For \( f(g(8)) \):

Step1: Find \( g(8) \)

From the table, when \( x = 8 \), \( g(8)=4 \).

Step2: Find \( f(4) \)

From the table, when \( x = 4 \), \( f(4)=2 \).

Step1: Find \( f(6) \)

From the table, when \( x = 6 \), \( f(6)=8 \).

Step2: Find \( g(8) \)

From the table, when \( x = 8 \), \( g(8)=4 \).

Step1: Find \( f(1) \)

From the table, when \( x = 1 \), \( f(1)=4 \).

Step2: Find \( f(4) \)

From the table, when \( x = 4 \), \( f(4)=2 \).

Answer:

\( 2 \)

For \( g(f(6)) \):