To solve for [tex]\((f - g)(144)\)[/tex] given [tex]\( f(x) = \sqrt{x} + 12 \)[/tex] and [tex]\( g(x) = 2 \sqrt{x} \)[/tex], we'll follow these steps:
1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 144 \)[/tex]:
[tex]\[
f(144) = \sqrt{144} + 12
\][/tex]
Knowing that [tex]\( \sqrt{144} = 12 \)[/tex], we substitute this value into the function:
[tex]\[
f(144) = 12 + 12
\][/tex]
[tex]\[
f(144) = 24
\][/tex]
2. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 144 \)[/tex]:
[tex]\[
g(144) = 2 \sqrt{144}
\][/tex]
Again, knowing that [tex]\( \sqrt{144} = 12 \)[/tex], we substitute this value into the function:
[tex]\[
g(144) = 2 \cdot 12
\][/tex]
[tex]\[
g(144) = 24
\][/tex]
3. Find the value of [tex]\((f-g)(144)\)[/tex]:
[tex]\[
(f-g)(144) = f(144) - g(144)
\][/tex]
Substituting the values we found:
[tex]\[
(f-g)(144) = 24 - 24
\][/tex]
[tex]\[
(f-g)(144) = 0
\][/tex]
Therefore, the value of [tex]\((f-g)(144)\)[/tex] is [tex]\( \boxed{0} \)[/tex].
