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The table shows values for the two functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex] for different values of [tex]\( x \)[/tex].

What is [tex]\( f(g(0)) \)[/tex]?

A. -1
B. 0
C. 1
D. This composition is undefined.

[tex]\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
-2 & 4 & -3 \\
\hline
-1 & 1 & -2 \\
\hline
0 & 0 & -1 \\
\hline
1 & 1 & 0 \\
\hline
2 & 4 & 1 \\
\hline
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To determine the value of [tex]\( f(g(0)) \)[/tex], we need to follow these steps:

1. Find [tex]\( g(0) \)[/tex]:
We will look up the value of the function [tex]\( g \)[/tex] when [tex]\( x = 0 \)[/tex] from the given table. According to the table:
[tex]\[ g(0) = -1 \][/tex]

2. Find [tex]\( f(g(0)) \)[/tex]:
Now that we know [tex]\( g(0) = -1 \)[/tex], the next step is to find the value of the function [tex]\( f \)[/tex] when [tex]\( x = -1 \)[/tex]. According to the table:
[tex]\[ f(-1) = 1 \][/tex]

Therefore, [tex]\( f(g(0)) = f(-1) = 1 \)[/tex].

So, the value of [tex]\( f(g(0)) \)[/tex] is [tex]\( 1 \)[/tex].
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