What values for x would make `(1)/(sqrt(x+1))` undefined ?

Options

A. `-1` only
B. 1 only
C. All real numbers greater than -1
D. All real numbers less than or equal to -1

Explanation

To determine the values for \( x \) that would make the expression \( \frac{1}{\sqrt{x+1}} \) undefined, we need to analyze the conditions under which the denominator becomes zero or the expression inside the square root becomes negative.

### Step-by-Step Solution:

1. **Identify the Denominator**: The expression is \( \frac{1}{\sqrt{x+1}} \). The denominator is \( \sqrt{x+1} \).

2. **Condition for Undefined Expression**: The expression is undefined when the denominator is zero. Therefore, we need to find when:
\[ \sqrt{x+1} = 0 \]

3. **Solve for \( x \)**: To find when the square root is zero, we set:
\[ x + 1 = 0 \]
Solving for \( x \) gives:
\[ x = -1 \]

4. **Condition for Square Root**: Additionally, the square root is only defined for non-negative values. Thus, we need:
\[ x + 1 \geq 0 \]
This simplifies to:
\[ x \geq -1 \]

5. **Combine Conditions**: The expression \( \frac{1}{\sqrt{x+1}} \) is undefined for:
- \( x = -1 \) (where the denominator becomes zero)
- \( x < -1 \) (where the expression under the square root becomes negative)

6. **Conclusion**: Therefore, the expression is undefined for all values of \( x \) that are less than or equal to -1.

### Final Answer:
The values for \( x \) that would make \( \frac{1}{\sqrt{x+1}} \) undefined are:
\[ x \leq -1 \]