Answered

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If [tex]$f(x) = 2x^2 - 5$[/tex] and [tex]$g(x) = 3x + 7$[/tex], find [tex]$[f \circ g](0)$[/tex].

A. 93
B. [tex]$-5$[/tex]
C. [tex]$-8$[/tex]
D. 195

Sagot :

GinnyAnswer
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]
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