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Given the following table of values, compute [tex]\((g \circ g)(-4)\)[/tex].

| [tex]\(x\)[/tex] | [tex]\(f(x)\)[/tex] | [tex]\(g(x)\)[/tex] |
|---|---|---|
| -4 | 2 | 3 |
| -3 | -4 | -1 |
| -2 | 0 | 1 |
| -1 | -2 | -4 |
| 0 | 1 | -3 |
| 1 | 3 | -2 |
| 2 | -1 | 4 |
| 3 | 4 | 0 |
| 4 | -3 | 2 |



Answer :

GinnyAnswer
To compute [tex]\( (g \circ g)(-4) \)[/tex], we need to perform function composition, applying the function [tex]\( g \)[/tex] twice.

1. Find [tex]\( g(-4) \)[/tex]:
- According to the table, [tex]\( g(-4) = 3 \)[/tex].

2. Next, find [tex]\( g(g(-4)) \)[/tex]:
- We now need to find [tex]\( g(3) \)[/tex].
- According to the table, [tex]\( g(3) = 0 \)[/tex].

Therefore, [tex]\( (g \circ g)(-4) = g(g(-4)) = g(3) = 0 \)[/tex].

Hence, the value of [tex]\( (g \circ g)(-4) \)[/tex] is [tex]\( 0 \)[/tex].

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