From everyday questions to specialized queries, IDNLearn.com has the answers. Ask any question and receive timely, accurate responses from our dedicated community of experts.
Sagot :
To determine [tex]\( f(a+2) \)[/tex] for the function [tex]\( f(x) = 3x + \frac{5}{x} \)[/tex], let's proceed step-by-step.
1. Substitute [tex]\(a+2\)[/tex] for [tex]\(x\)[/tex] in the function [tex]\( f(x) \)[/tex]:
Given:
[tex]\[ f(x) = 3x + \frac{5}{x} \][/tex]
We need to find [tex]\( f(a+2) \)[/tex]. So substitute [tex]\(a+2\)[/tex] for [tex]\(x\)[/tex] in [tex]\( f(x) \)[/tex]:
[tex]\[ f(a+2) = 3(a+2) + \frac{5}{a+2} \][/tex]
2. Simplify the expression:
- First, distribute the 3 inside the parentheses:
[tex]\[ 3(a+2) = 3a + 6 \][/tex]
- The term [tex]\(\frac{5}{a+2}\)[/tex] remains as is.
3. Combine the terms:
So the entire expression for [tex]\( f(a+2) \)[/tex] becomes:
[tex]\[ f(a+2) = 3a + 6 + \frac{5}{a+2} \][/tex]
This is our final, simplified expression.
Given the choices:
- A: [tex]\( 3(a+2) + \frac{5}{a+2} \)[/tex]
- B: [tex]\( 3a + \frac{5}{a} + 2 \)[/tex]
- C: [tex]\( 3(f(a)) + \frac{5}{f(a) + 2} \)[/tex]
The correct answer is:
A. [tex]\( 3(a+2) + \frac{5}{a+2} \)[/tex]
However, simplifying this result further as we did above should match the expression:
[tex]\[ 3a + 6 + \frac{5}{a+2} \][/tex]
This confirms our answer.
1. Substitute [tex]\(a+2\)[/tex] for [tex]\(x\)[/tex] in the function [tex]\( f(x) \)[/tex]:
Given:
[tex]\[ f(x) = 3x + \frac{5}{x} \][/tex]
We need to find [tex]\( f(a+2) \)[/tex]. So substitute [tex]\(a+2\)[/tex] for [tex]\(x\)[/tex] in [tex]\( f(x) \)[/tex]:
[tex]\[ f(a+2) = 3(a+2) + \frac{5}{a+2} \][/tex]
2. Simplify the expression:
- First, distribute the 3 inside the parentheses:
[tex]\[ 3(a+2) = 3a + 6 \][/tex]
- The term [tex]\(\frac{5}{a+2}\)[/tex] remains as is.
3. Combine the terms:
So the entire expression for [tex]\( f(a+2) \)[/tex] becomes:
[tex]\[ f(a+2) = 3a + 6 + \frac{5}{a+2} \][/tex]
This is our final, simplified expression.
Given the choices:
- A: [tex]\( 3(a+2) + \frac{5}{a+2} \)[/tex]
- B: [tex]\( 3a + \frac{5}{a} + 2 \)[/tex]
- C: [tex]\( 3(f(a)) + \frac{5}{f(a) + 2} \)[/tex]
The correct answer is:
A. [tex]\( 3(a+2) + \frac{5}{a+2} \)[/tex]
However, simplifying this result further as we did above should match the expression:
[tex]\[ 3a + 6 + \frac{5}{a+2} \][/tex]
This confirms our answer.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.