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If [tex]f(x) = \sqrt{x} + 12[/tex] and [tex]g(x) = 2 \sqrt{x}[/tex], what is the value of [tex](f-g)(144)[/tex]?

A. -84
B. -60
C. 0
D. 48

Sagot :

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]