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Given the function [tex]\( f(x) = 3(x+5) + \frac{4}{x} \)[/tex], what is [tex]\( f(a+2) \)[/tex]?

A. [tex]\( 3(f(a)+5) + \frac{4}{f(a)+2} \)[/tex]

B. [tex]\( 3(a+2) + \frac{4}{a} + 2 \)[/tex]

C. [tex]\( 3(a+7) + \frac{4}{a+2} \)[/tex]

Sagot :

GinnyAnswer
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]
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