To solve for [tex]\((f-g)(144)\)[/tex], we first need to determine the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
- [tex]\(f(x) = \sqrt{x} + 12\)[/tex]
- [tex]\(g(x) = 2 \sqrt{x}\)[/tex]
Next, we need to evaluate these functions at [tex]\(x = 144\)[/tex].
First, evaluate [tex]\(f(144)\)[/tex]:
[tex]\[
f(144) = \sqrt{144} + 12
\][/tex]
We know that [tex]\(\sqrt{144} = 12\)[/tex], so:
[tex]\[
f(144) = 12 + 12 = 24
\][/tex]
Now, evaluate [tex]\(g(144)\)[/tex]:
[tex]\[
g(144) = 2 \sqrt{144}
\][/tex]
Again, knowing that [tex]\(\sqrt{144} = 12\)[/tex], we get:
[tex]\[
g(144) = 2 \times 12 = 24
\][/tex]
Now we need to find [tex]\((f - g)(144)\)[/tex]:
[tex]\[
(f - g)(144) = f(144) - g(144)
\][/tex]
Substitute the values we found:
[tex]\[
(f - g)(144) = 24 - 24 = 0
\][/tex]
Therefore, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\( \boxed{0} \)[/tex].
