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]
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]
