To find the value of [tex]\((f - g)(144)\)[/tex] given the functions [tex]\(f(x) = \sqrt{x} + 12\)[/tex] and [tex]\(g(x) = 2\sqrt{x}\)[/tex], follow these steps:
1. Evaluate [tex]\(f(x)\)[/tex] for [tex]\(x = 144\)[/tex]:
[tex]\[
f(144) = \sqrt{144} + 12
\][/tex]
Since [tex]\(\sqrt{144} = 12\)[/tex],
[tex]\[
f(144) = 12 + 12 = 24
\][/tex]
2. Evaluate [tex]\(g(x)\)[/tex] for [tex]\(x = 144\)[/tex]:
[tex]\[
g(144) = 2 \sqrt{144}
\][/tex]
Since [tex]\(\sqrt{144} = 12\)[/tex],
[tex]\[
g(144) = 2 \times 12 = 24
\][/tex]
3. Compute [tex]\((f - g)(144)\)[/tex]:
[tex]\[
(f - g)(144) = f(144) - g(144)
\][/tex]
Substituting the values obtained,
[tex]\[
(f - g)(144) = 24 - 24 = 0
\][/tex]
Thus, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\(\boxed{0}\)[/tex].
