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Use the table to evaluate the expression.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline [tex]$x$[/tex] & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline [tex]$f(x)$[/tex] & 2 & 3 & 5 & 1 & 6 & 3 \\
\hline [tex]$g(x)$[/tex] & 3 & 5 & 1 & 6 & 4 & 2 \\
\hline
\end{tabular}

Evaluate: [tex]$(g \circ f)(2)$[/tex]

Sagot :

GinnyAnsweridn
To solve the expression [tex]\((g \circ f)(2)\)[/tex], we need to evaluate the value of the function [tex]\(g\)[/tex] at the point [tex]\(f(2)\)[/tex]. We will use the values provided in the table to do this step-by-step.

Step 1: Evaluate [tex]\(f(2)\)[/tex]
- From the table, we see that when [tex]\(x = 2\)[/tex], [tex]\(f(x) = 3\)[/tex].
- Therefore, [tex]\(f(2) = 3\)[/tex].

Step 2: Evaluate [tex]\(g(f(2))\)[/tex]
- From Step 1, we know [tex]\(f(2) = 3\)[/tex]. So, we need to find [tex]\(g(3)\)[/tex].
- From the table, we see that when [tex]\(x = 3\)[/tex], [tex]\(g(x) = 1\)[/tex].
- Therefore, [tex]\(g(3) = 1\)[/tex].

Putting it all together, we get:
[tex]\[ (g \circ f)(2) = g(f(2)) = g(3) = 1 \][/tex]

Therefore, the value of the expression [tex]\((g \circ f)(2)\)[/tex] is [tex]\(1\)[/tex].
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