To find [tex]\((f \circ g)(2)\)[/tex], we need to evaluate the composition of the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] at the input value [tex]\(2\)[/tex]. The composition [tex]\((f \circ g)(2)\)[/tex] means [tex]\(f(g(2))\)[/tex].
Here are the steps to find [tex]\((f \circ g)(2)\)[/tex]:
1. Evaluate [tex]\(g(2)\)[/tex]:
According to the information given,
[tex]\[
g(2) = -11
\][/tex]
2. Substitute [tex]\(g(2)\)[/tex] into [tex]\(f\)[/tex]:
Since [tex]\(g(2) = -11\)[/tex], we now need to find [tex]\(f(-11)\)[/tex].
3. Evaluate [tex]\(f(-11)\)[/tex]:
According to the information given,
[tex]\[
f(-11) = -6
\][/tex]
Therefore, [tex]\((f \circ g)(2) = f(g(2)) = f(-11) = -6\)[/tex].
So, the value of [tex]\((f \circ g)(2)\)[/tex] is [tex]\(-6\)[/tex].
