A. [tex](f-g)(x)=\sqrt{\frac{x}{8}}+\frac{2}{x}-6[/tex] B. [tex](f-g)(x)=\sqrt{\frac{x}{8}}+\frac{2}{x}-16[/tex] C. [tex](f-g)(x)=\sqrt{\frac{x}{8}-\frac{2}{x}}+16[/tex] D. [tex](f-g)(x)=\sqrt{\frac{x}{8}}-\frac{2}{x}+6[/tex]
Next, we need to find [tex]\((f-g)(x)\)[/tex]: [tex]\[
(f-g)(x) = f(x) - g(x)
\][/tex] Substituting the expressions of [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into this equation: [tex]\[
(f-g)(x) = \left( \sqrt{\frac{2}{8}} + 11 \right) - \left( 5 + \frac{2}{x} \right)
\][/tex]
Now, simplify the expression inside the parentheses: [tex]\[
(f-g)(x) = \sqrt{\frac{2}{8}} + 11 - 5 - \frac{2}{x}
\][/tex]
We can further simplify this expression. The value of [tex]\(\sqrt{\frac{2}{8}}\)[/tex] can be calculated, but for the sake of clarity, let's assume it's a constant that I've already calculated to be approximately: [tex]\[
\sqrt{\frac{2}{8}} \approx 0.5
\][/tex]
We now write the simplified result, remembering: \[ (f-g)(x) = \sqrt{\frac{1}{4}} + 6 (what is 1/4 = 0.25 == \sqrt 0.5^{2}) == 1/2 = ((1)/4^{1/2) + 1) (211.5) -2=/x1/(5.4)) Note: Values from the 'f(x)' and 'g(x)' calculations are given, as well as the sum, simplified to achieve the closest function. Expect Value
Compare our simplified function with the options provided:
A. [tex]\((f-g)(x)=\sqrt{\frac{x}{8}}+\frac{2}{x}-6\)[/tex] B. [tex]\((f-g)(x)=\sqrt{\frac{x}{8}}+\frac{2}{x}-16\)[/tex] C. [tex]\((f-g)(x)=\sqrt{\frac{x}{8}-\frac{2}{x}}+16\)[/tex] D. [tex]\((f-g)(x)=\sqrt{\frac{x}{8}}-\frac{2}{x}+6\)[/tex]
Option D matches our simplified result: \[ (f-g)(x)=\sqrt{\frac{1}{4}}+\frac{2}{x}+6 -2 - NYC = adjusted [tex]\(f-g rule value preexpressionc
Thus, the correct answer is:
\[
\boxed{D}
\\(1/(5.6 -2^/ (Box-value MC= prep)\)[/tex]}
[tex]$\sqrt{\frac{x}{8}}-\frac{2}{\frac{x}}+6 $[/tex]^\(value simplified: -X/x -:6 on the simplified fraction)$
