Answer :
To solve for [tex]\( f(a+2) \)[/tex] given the function [tex]\( f(x) = 3(x + 5) + \frac{4}{x} \)[/tex], let's break this down step-by-step.
1. Identify the original function:
[tex]\[ f(x) = 3(x + 5) + \frac{4}{x} \][/tex]
2. Substitute [tex]\( a+2 \)[/tex] for [tex]\( x \)[/tex]:
[tex]\[ f(a+2) = 3((a+2) + 5) + \frac{4}{a+2} \][/tex]
3. Simplify inside the parentheses first:
[tex]\[ (a+2) + 5 = a + 7 \][/tex]
4. Substitute this simplified expression back into the function:
[tex]\[ f(a+2) = 3(a+7) + \frac{4}{a+2} \][/tex]
So, the function evaluated at [tex]\( a+2 \)[/tex] is:
[tex]\[ f(a+2) = 3(a+7) + \frac{4}{a+2} \][/tex]
Now, we match this result with the given options:
- Option A: [tex]\( 3(a+7) + \frac{4}{a+2} \)[/tex]
- Option B: [tex]\( 3(a+2) + \frac{4}{a} + 2 \)[/tex]
- Option C: [tex]\( 3(f(a)+5) + \frac{4}{f(a)+2} \)[/tex]
The correct answer is:
[tex]\[ \boxed{A} \][/tex]
1. Identify the original function:
[tex]\[ f(x) = 3(x + 5) + \frac{4}{x} \][/tex]
2. Substitute [tex]\( a+2 \)[/tex] for [tex]\( x \)[/tex]:
[tex]\[ f(a+2) = 3((a+2) + 5) + \frac{4}{a+2} \][/tex]
3. Simplify inside the parentheses first:
[tex]\[ (a+2) + 5 = a + 7 \][/tex]
4. Substitute this simplified expression back into the function:
[tex]\[ f(a+2) = 3(a+7) + \frac{4}{a+2} \][/tex]
So, the function evaluated at [tex]\( a+2 \)[/tex] is:
[tex]\[ f(a+2) = 3(a+7) + \frac{4}{a+2} \][/tex]
Now, we match this result with the given options:
- Option A: [tex]\( 3(a+7) + \frac{4}{a+2} \)[/tex]
- Option B: [tex]\( 3(a+2) + \frac{4}{a} + 2 \)[/tex]
- Option C: [tex]\( 3(f(a)+5) + \frac{4}{f(a)+2} \)[/tex]
The correct answer is:
[tex]\[ \boxed{A} \][/tex]
