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Let's analyze and solve the questions visible in the uploaded image step by step. The task involves finding the functions \( f + g \), \( f - g \), \( f \circ g \), and \( f / g \), as well as determining their respective domains. The given functions are:

- \( f(x) = x \)
- \( g(x) = \sqrt{x} \)

---

### Step 1: \( (f + g)(x) \) and its domain
#### Formula:
\[
(f + g)(x) = f(x) + g(x) = x + \sqrt{x}
\]

#### Domain:
- \( \sqrt{x} \) is defined when \( x \geq 0 \).
- Therefore, the domain of \( (f + g)(x) \) is \( [0, \infty) \).

---

### Step 2: \( (f - g)(x) \) and its domain
#### Formula:
\[
(f - g)(x) = f(x) - g(x) = x - \sqrt{x}
\]

#### Domain:
- The same condition applies as for \( g(x) = \sqrt{x} \): \( x \geq 0 \).
- Thus, the domain of \( (f - g)(x) \) is \( [0, \infty) \).

---

### Step 3: \( (f \circ g)(x) \) and its domain
#### Formula:
\[
(f \circ g)(x) = f(g(x)) = f(\sqrt{x}) = \sqrt{x}
\]

#### Domain:
- \( g(x) = \sqrt{x} \) requires \( x \geq 0 \), so the domain of \( f \circ g \) is \( [0, \infty) \).

---

### Step 4: \( (f / g)(x) \) and its domain
#### Formula:
\[
\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{x}{\sqrt{x}}
\]

Simplify:
\[
\left(\frac{f}{g}\right)(x) = \sqrt{x} \quad \text{(for \( x > 0 \))}.
\]

#### Domain:
- \( g(x) = \sqrt{x} \) must be nonzero, which implies \( x > 0 \).
- Therefore, the domain of \( \frac{f}{g}(x) \) is \( (0, \infty) \).

---

### Final Results:
1. \( (f + g)(x) = x + \sqrt{x}, \quad \text{domain: } [0, \infty) \).
2. \( (f - g)(x) = x - \sqrt{x}, \quad \text{domain: } [0, \infty) \).
3. \( (f \circ g)(x) = \sqrt{x}, \quad \text{domain: } [0, \infty) \).
4. \( \left(\frac{f}{g}\right)(x) = \sqrt{x}, \quad \text{domain: } (0, \infty) \).

Would you like additional steps or clarifications? Here are some related questions you might explore:

1. What is the graph of \( f(x) + g(x) \) in its domain?
2. How do operations on \( f(x) \) and \( g(x) \) affect their domains?
3. How can you compute \( (g \circ f)(x) \) instead of \( (f \circ g)(x) \)?
4. What happens to \( \frac{f}{g} \) if \( g(x) \) equals zero?
5. How can this problem generalize for other types of functions \( f(x) \) and \( g(x) \)?

**Tip:** When finding the domain of a composite function, always consider both the domain of the inner and the outer function.

Find f + g, f - g, f ∘ g, and f/g and their domains. The given functions are f(x) = x and g(x) = √x.

Explore how to perform function operations (addition, subtraction, composition, and division) for f(x) = x and g(x) = √x. Learn about determining the domains of each operation, focusing on key algebraic principles and properties of square root functions. Suitable for high school math students.

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