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].
