Let's solve the problem step by step in a clear manner.
1. Functions Definition:
We have two functions given:
[tex]\[
f(x) = \sqrt{x} + 12
\][/tex]
and
[tex]\[
g(x) = 2 \sqrt{x}
\][/tex]
2. Finding Specific Values:
We are asked to find the value of [tex]\((f - g)(144)\)[/tex].
3. Individual Function Calculations:
First, we need to determine the values of [tex]\(f(144)\)[/tex] and [tex]\(g(144)\)[/tex].
- For [tex]\(f(x)\)[/tex]:
[tex]\[
f(144) = \sqrt{144} + 12
\][/tex]
- Since [tex]\(\sqrt{144} = 12\)[/tex]:
[tex]\[
f(144) = 12 + 12 = 24
\][/tex]
- For [tex]\(g(x)\)[/tex]:
[tex]\[
g(144) = 2 \sqrt{144}
\][/tex]
- Because [tex]\(\sqrt{144} = 12\)[/tex]:
[tex]\[
g(144) = 2 \times 12 = 24
\][/tex]
4. Subtraction of Functions:
Now, we compute [tex]\((f - g)(144)\)[/tex]:
[tex]\[
(f - g)(144) = f(144) - g(144)
\][/tex]
Substituting the values we found:
[tex]\[
(f - g)(144) = 24 - 24 = 0
\][/tex]
Thus, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\(0\)[/tex].
The correct answer is:
[tex]\[
\boxed{0}
\][/tex]
