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If [tex]\( f(x) = 3x + \frac{5}{x} \)[/tex], what is [tex]\( f(a+2) \)[/tex]?

A. [tex]\( 3(f(a)) + \frac{5}{f(a)+2} \)[/tex]
B. [tex]\( 3(a+2) + \frac{5}{a+2} \)[/tex]
C. [tex]\( 3a + \frac{5}{-2} \)[/tex]

Sagot :

GinnyAnswer
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]
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