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------------------------------------------------ If [tex]$f(x) = 2x + 3$[/tex] and [tex]$g(x) = x^2 + 1$[/tex], find [tex][tex]$f(g(3))$[/tex][/tex].

A. 23
B. 47
C. 82
D. 90

Answer :

Let's solve the problem step-by-step.

Given:
- [tex]\( f(x) = 2x + 3 \)[/tex]
- [tex]\( g(x) = x^2 + 1 \)[/tex]

We need to find [tex]\( f(g(3)) \)[/tex].

1. First, calculate [tex]\( g(3) \)[/tex].
[tex]\[
g(x) = x^2 + 1
\][/tex]
So,
[tex]\[
g(3) = 3^2 + 1 = 9 + 1 = 10
\][/tex]

2. Then, use the result from [tex]\( g(3) \)[/tex] to find [tex]\( f(g(3)) \)[/tex].
[tex]\[
f(x) = 2x + 3
\][/tex]
Here, we have [tex]\( x = g(3) = 10 \)[/tex].

So,
[tex]\[
f(10) = 2(10) + 3 = 20 + 3 = 23
\][/tex]

Therefore, the value of [tex]\( f(g(3)) \)[/tex] is [tex]\( 23 \)[/tex].

The correct answer is [tex]\(\boxed{23}\)[/tex].

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