To evaluate [tex]\((f \circ g)(-11)\)[/tex], we need to go through the following steps:
1. Calculate [tex]\( g(-11) \)[/tex]:
The function [tex]\( g(c) \)[/tex] is defined as:
[tex]\[
g(c) = \sqrt{14 - c}
\][/tex]
Substituting [tex]\( c = -11 \)[/tex], we get:
[tex]\[
g(-11) = \sqrt{14 - (-11)} = \sqrt{14 + 11} = \sqrt{25} = 5.0
\][/tex]
Thus, [tex]\( g(-11) = 5.0 \)[/tex].
2. Calculate [tex]\( f(g(-11)) \)[/tex]:
We have already found that [tex]\( g(-11) = 5.0 \)[/tex]. Now, we need to evaluate the function [tex]\( f(c) \)[/tex] at [tex]\( c = 5.0 \)[/tex].
The function [tex]\( f(c) \)[/tex] is defined as:
[tex]\[
f(c) = 3c - 8
\][/tex]
Substituting [tex]\( c = 5.0 \)[/tex], we get:
[tex]\[
f(5.0) = 3(5.0) - 8 = 15.0 - 8 = 7.0
\][/tex]
So, [tex]\((f \circ g)(-11) = f(g(-11)) = 7.0\)[/tex].
The final answers are:
[tex]\[
g(-11) = 5.0
\][/tex]
[tex]\[
(f \circ g)(-11) = 7.0
\][/tex]
