The expression given is \(\sqrt{x^2 - 5} + 4\). 

This is a square root function with a constant added to it. The expression inside the square root is \(x^2 - 5\), and then you add 4 to the result of the square root.

### Steps to analyze:

1. **Expression inside the square root:**
   \[
   x^2 - 5
   \]
   This must be non-negative for the square root to be real. Therefore, 
   \[
   x^2 - 5 \geq 0
   \]
   Solving this inequality:
   \[
   x^2 \geq 5
   \]
   \[
   x \geq \sqrt{5} \quad \text{or} \quad x \leq -\sqrt{5}
   \]
   So, \(x\) must be outside the interval \((- \sqrt{5}, \sqrt{5})\).

2. **Adding 4:**
   After calculating \(\sqrt{x^2 - 5}\), 4 is simply added to the result.

The final expression doesn't simplify further without a specific value for \(x\).

### Summary:
The expression \(\sqrt{x^2 - 5} + 4\) is defined for \(x \leq -\sqrt{5}\) or \(x \geq \sqrt{5}\).

Would you like any additional details or have any specific questions?

### Related Questions:
1. How does the graph of \(\sqrt{x^2 - 5} + 4\) look?
2. What is the domain of \(\sqrt{x^2 - 5}\)?
3. How do you solve \(\sqrt{x^2 - 5} + 4 = 0\)?
4. Can \(\sqrt{x^2 - 5} + 4\) ever be negative?
5. What is the range of the function \(\sqrt{x^2 - 5} + 4\)?

**Tip:** When dealing with square roots, always consider the domain to ensure the expression inside the square root is non-negative.

Explore the function √(x² - 5) + 4 with a step-by-step analysis. Learn about its domain and the conditions under which it is defined. Suitable for high school students studying square root functions and inequalities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation