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If [tex]$f(x)=\sqrt{x}+12$[/tex] and [tex]$g(x)=2\sqrt{x}$[/tex], what is the value of [tex][tex]$(f-g)(144)$[/tex][/tex]?

A. [tex]-84[/tex]
B. [tex]-60[/tex]
C. [tex]0[/tex]
D. [tex]48[/tex]


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].