https://file.aiquickdraw.com/mathbot/file/1722865303369a1pg3j5p.jpg

f(x)= 1/2x and g(x)= 4/x+12 find (f+g)(x)

To find \((f + g)(x)\) given the functions \(f(x) = \frac{1}{2x}\) and \(g(x) = \frac{4}{x} + 12\), follow these steps:

1. **Write down the given functions:**
   - \( f(x) = \frac{1}{2x} \)
   - \( g(x) = \frac{4}{x} + 12 \)

2. **Add the two functions:**
   \[
   (f + g)(x) = f(x) + g(x)
   \]
   Substitute the given functions:
   \[
   (f + g)(x) = \frac{1}{2x} + \left(\frac{4}{x} + 12\right)
   \]

3. **Combine the fractions:**
   To combine the fractions, find a common denominator. The common denominator for \(2x\) and \(x\) is \(2x\):
   \[
   (f + g)(x) = \frac{1}{2x} + \frac{4}{x} + 12
   \]
   Rewrite \(\frac{4}{x}\) with the common denominator:
   \[
   \frac{4}{x} = \frac{4 \cdot 2}{x \cdot 2} = \frac{8}{2x}
   \]
   Now combine the fractions:
   \[
   (f + g)(x) = \frac{1}{2x} + \frac{8}{2x} + 12
   \]
   Add the fractions:
   \[
   (f + g)(x) = \frac{1 + 8}{2x} + 12 = \frac{9}{2x} + 12
   \]

So, the function \((f + g)(x)\) is:
\[
(f + g)(x) = \frac{9}{2x} + 12
\]

Would you like further details or have any questions about this solution?

Here are some related questions you might find useful:

1. How do you find \((f - g)(x)\) given \(f(x) = \frac{1}{2x}\) and \(g(x) = \frac{4}{x} + 12\)?
2. What is the domain of \((f + g)(x)\) for the given functions?
3. How do you find \((fg)(x)\) given \(f(x) = \frac{1}{2x}\) and \(g(x) = \frac{4}{x} + 12\)?
4. How do you find \((f / g)(x)\) given \(f(x) = \frac{1}{2x}\) and \(g(x) = \frac{4}{x} + 12\)?
5. How do you determine if the functions \(f(x)\) and \(g(x)\) are inverses of each other?
6. How do you find the derivative of \((f + g)(x)\) for the given functions?
7. What are the vertical asymptotes of \((f + g)(x)\)?
8. How would you find the integral of \((f + g)(x)\)?

**Tip:** When adding or subtracting rational functions, always find a common denominator to simplify the process.

Learn how to add rational functions (f+g)(x) = 1/(2x) + (4/x + 12) with a step-by-step solution. This problem involves adding fractions with different denominators and simplifying the result. Suitable for high school students studying functions and rational expressions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation