To solve for [tex]\( f(a+2) \)[/tex] in the function [tex]\( f(x) = 3x + \frac{5}{x} \)[/tex], please follow these steps:
1. Substitute [tex]\( a+2 \)[/tex] in place of [tex]\( x \)[/tex] in the function:
[tex]\[
f(a+2) = 3(a+2) + \frac{5}{a+2}
\][/tex]
2. Simplify the expression:
[tex]\[
f(a+2) = 3(a+2) + \frac{5}{a+2}
\][/tex]
This is already in its simplest form, as it directly substitutes [tex]\( a+2 \)[/tex] into the given function [tex]\( f(x) \)[/tex].
According to our calculations, comparing the expression [tex]\( 3(a+2) + \frac{5}{a+2} \)[/tex] with the given options, we see that it matches option B.
Therefore, the correct answer is:
[tex]\[
\boxed{3(a+2) + \frac{5}{a+2}}
\][/tex]
