To determine the value of [tex]\((f - g)(144)\)[/tex] given the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], follow these steps:
1. Define the functions:
- [tex]\( f(x) = \sqrt{x} + 12 \)[/tex]
- [tex]\( g(x) = 2 \sqrt{x} \)[/tex]
2. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 144 \)[/tex]:
- Calculate [tex]\( \sqrt{144} \)[/tex]:
[tex]\[
\sqrt{144} = 12
\][/tex]
- Substitute [tex]\( \sqrt{144} \)[/tex] back into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(144) = 12 + 12 = 24.0
\][/tex]
3. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 144 \)[/tex]:
- Calculate [tex]\( 2 \sqrt{144} \)[/tex]:
[tex]\[
2 \cdot \sqrt{144} = 2 \cdot 12 = 24.0
\][/tex]
4. Calculate [tex]\((f - g)(144)\)[/tex]:
- Subtract [tex]\( g(144) \)[/tex] from [tex]\( f(144) \)[/tex]:
[tex]\[
(f - g)(144) = f(144) - g(144) = 24.0 - 24.0 = 0.0
\][/tex]
Therefore, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\( 0 \)[/tex]. The correct answer is:
[tex]\[ 0 \][/tex]
