Given [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. [tex]\(-84\)[/tex]
B. [tex]\(-60\)[/tex]
C. [tex]\(0\)[/tex]
D. [tex]\(48\)[/tex]



Answer :

To solve the problem, we need to determine the value of [tex]\( (f-g)(144) \)[/tex].

Let's start by evaluating the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] at [tex]\( x = 144 \)[/tex].

First, consider the function [tex]\( f(x) = \sqrt{x} + 12 \)[/tex]:

1. Find [tex]\( f(144) \)[/tex]:
[tex]\[ f(144) = \sqrt{144} + 12 \][/tex]
Since [tex]\( \sqrt{144} = 12 \)[/tex]:
[tex]\[ f(144) = 12 + 12 = 24.0 \][/tex]

Next, consider the function [tex]\( g(x) = 2 \sqrt{x} \)[/tex]:

2. Find [tex]\( g(144) \)[/tex]:
[tex]\[ g(144) = 2 \sqrt{144} \][/tex]
Since [tex]\( \sqrt{144} = 12 \)[/tex]:
[tex]\[ g(144) = 2 \cdot 12 = 24.0 \][/tex]

Finally, to find [tex]\( (f-g)(144) \)[/tex], we subtract [tex]\( g(144) \)[/tex] from [tex]\( f(144) \)[/tex]:

3. Calculate [tex]\( (f-g)(144) \)[/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].

So, the correct answer is:
[tex]\[ \boxed{0} \][/tex]