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Which function defines [tex](f+g)(x)[/tex]?
[tex]\[
\begin{array}{l}
f(x)=\frac{5}{x}+12 \\
g(x)=\sqrt{x-3}+10
\end{array}
\][/tex]

A. [tex](f+g)(x)=\frac{5}{x}-\sqrt{x-3}+2[/tex]
B. [tex](f+g)(x)=\frac{\sqrt{x-3}+5}{x}+22[/tex]
C. [tex](f+g)(x)=\frac{5}{x}+\sqrt{x}+19[/tex]
D. [tex](f+g)(x)=\frac{5}{x}+\sqrt{x-3}+22[/tex]

Sagot :

GinnyAnsweridn
To solve for [tex]\((f+g)(x)\)[/tex], we need to add the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] together.

Given:
[tex]\[ f(x) = \frac{5}{x} + 12 \][/tex]
[tex]\[ g(x) = \sqrt{x-3} + 10 \][/tex]

We then define [tex]\((f+g)(x)\)[/tex] as follows:
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]

Substituting the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ (f+g)(x) = \left( \frac{5}{x} + 12 \right) + \left( \sqrt{x-3} + 10 \right) \][/tex]

Combine the terms:
[tex]\[ (f+g)(x) = \frac{5}{x} + 12 + \sqrt{x-3} + 10 \][/tex]
[tex]\[ (f+g)(x) = \frac{5}{x} + \sqrt{x-3} + 12 + 10 \][/tex]
[tex]\[ (f+g)(x) = \frac{5}{x} + \sqrt{x-3} + 22 \][/tex]

Now, we compare this function with the given options:

A. [tex]\(\frac{5}{x} - \sqrt{x-3} + 2\)[/tex]

B. [tex]\(\frac{\sqrt{x-3} + 5}{x} + 22\)[/tex]

C. [tex]\(\frac{5}{x} + \sqrt{x} + 19\)[/tex]

D. [tex]\(\frac{5}{x} + \sqrt{x-3} + 22\)[/tex]

The correct function is:

D. [tex]\((f+g)(x) = \frac{5}{x} + \sqrt{x-3} + 22\)[/tex]
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