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Sagot :
Let's solve for 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].
1. Evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 144\)[/tex]:
[tex]\[ f(144) = \sqrt{144} + 12 \][/tex]
[tex]\[ \sqrt{144} = 12 \][/tex]
[tex]\[ f(144) = 12 + 12 = 24 \][/tex]
2. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 144\)[/tex]:
[tex]\[ g(144) = 2\sqrt{144} \][/tex]
[tex]\[ \sqrt{144} = 12 \][/tex]
[tex]\[ g(144) = 2 \cdot 12 = 24 \][/tex]
3. Calculate [tex]\((f - g)(x)\)[/tex] at [tex]\(x = 144\)[/tex]:
[tex]\[ (f - g)(144) = f(144) - g(144) \][/tex]
[tex]\[ (f - g)(144) = 24 - 24 = 0 \][/tex]
So, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\(\boxed{0}\)[/tex].
1. Evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = 144\)[/tex]:
[tex]\[ f(144) = \sqrt{144} + 12 \][/tex]
[tex]\[ \sqrt{144} = 12 \][/tex]
[tex]\[ f(144) = 12 + 12 = 24 \][/tex]
2. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = 144\)[/tex]:
[tex]\[ g(144) = 2\sqrt{144} \][/tex]
[tex]\[ \sqrt{144} = 12 \][/tex]
[tex]\[ g(144) = 2 \cdot 12 = 24 \][/tex]
3. Calculate [tex]\((f - g)(x)\)[/tex] at [tex]\(x = 144\)[/tex]:
[tex]\[ (f - g)(144) = f(144) - g(144) \][/tex]
[tex]\[ (f - g)(144) = 24 - 24 = 0 \][/tex]
So, the value of [tex]\((f - g)(144)\)[/tex] is [tex]\(\boxed{0}\)[/tex].
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