To find [tex]\([f \circ g](0)\)[/tex], also written as [tex]\( f(g(0)) \)[/tex], we'll follow these steps:
1. Evaluate [tex]\( g(0) \)[/tex]:
- Given: [tex]\( g(x) = 3x + 7 \)[/tex].
- Substitute [tex]\( x = 0 \)[/tex]:
[tex]\[
g(0) = 3 \cdot 0 + 7 = 7
\][/tex]
2. Evaluate [tex]\( f(g(0)) \)[/tex], which is [tex]\( f(7) \)[/tex]:
- Given: [tex]\( f(x) = 2x^2 - 5 \)[/tex].
- Substitute [tex]\( x = 7 \)[/tex]:
[tex]\[
f(7) = 2 \cdot (7)^2 - 5
\][/tex]
[tex]\[
(7)^2 = 49
\][/tex]
[tex]\[
2 \cdot 49 = 98
\][/tex]
[tex]\[
98 - 5 = 93
\][/tex]
Thus, [tex]\([f \circ g](0) = 93\)[/tex].
The correct answer is:
[tex]\[ 93 \][/tex]
