https://file.aiquickdraw.com/mathbot/file/1727890095376jbr031ks.jpg

Let's address the two problems from the image, based on the provided functions:

We are given the following functions:
- \( f(x) = \sqrt{x} \)
- \( g(x) = \frac{x + 1}{x + 2} \)
- \( h(x) = |x - 1| \)

### Problem 1: \( (f + g)(3) \)

To solve \( (f + g)(3) \), we first evaluate each function separately at \( x = 3 \), and then add their results:

1. **Evaluate \( f(3) \):**
   \[
   f(3) = \sqrt{3}
   \]

2. **Evaluate \( g(3) \):**
   \[
   g(3) = \frac{3 + 1}{3 + 2} = \frac{4}{5}
   \]

Now, add the two values:
\[
(f + g)(3) = f(3) + g(3) = \sqrt{3} + \frac{4}{5}
\]
This is the simplified form of \( (f + g)(3) \).

---

### Problem 2: \( (f \circ h)(-3) \)

To solve \( (f \circ h)(-3) \), we first compute \( h(-3) \), and then use that result as the input for \( f \).

1. **Evaluate \( h(-3) \):**
   \[
   h(-3) = |-3 - 1| = |-4| = 4
   \]

2. **Evaluate \( f(4) \):**
   \[
   f(4) = \sqrt{4} = 2
   \]

Thus, \( (f \circ h)(-3) = f(h(-3)) = 2 \).

---

Would you like further clarification on any part of this? Here are some related questions for practice:

1. What is \( (f \cdot g)(2) \)?
2. Can you compute \( (g \circ h)(1) \)?
3. What is the value of \( (f + h)(0) \)?
4. What happens when you compute \( (g \circ f)(4) \)?
5. How do you interpret the behavior of \( f(x) \) as \( x \to 0 \)?

**Tip:** When evaluating compositions of functions, work from the inside out, starting with the innermost function and then applying the outer function.

Evaluate the indicated expression assuming that f(x) = √x, g(x) = (x + 1) / (x + 2), h(x) = |x - 1|. Solve: (f + g)(3) and (f o h)(-3).

Learn how to evaluate function addition and composition using the functions f(x) = √x, g(x) = (x + 1)/(x + 2), and h(x) = |x - 1|. The detailed step-by-step solutions cover solving (f + g)(3) and (f o h)(-3). Suitable for students in Grades 9-12.

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