Given the function [tex]\( f(x) = 3(x + 5) + \frac{4}{x} \)[/tex], we are required to find [tex]\( f(a + 2) \)[/tex].
To do this, we substitute [tex]\( a + 2 \)[/tex] for [tex]\( x \)[/tex] in the function [tex]\( f(x) \)[/tex].
Starting with the function [tex]\( f(x) = 3(x + 5) + \frac{4}{x} \)[/tex], we substitute [tex]\( x = a + 2 \)[/tex]:
[tex]\[ f(a + 2) = 3\left((a + 2) + 5\right) + \frac{4}{a + 2} \][/tex]
Simplify the expression inside the parentheses first:
[tex]\[ (a + 2) + 5 = a + 7 \][/tex]
Therefore, we have:
[tex]\[ f(a + 2) = 3(a + 7) + \frac{4}{a + 2} \][/tex]
So, the correct answer is:
C. [tex]\( 3(a + 7) + \frac{4}{a + 2} \)[/tex]
