Find the domain of $$ \mathrm{f}(\mathrm{x}) $$. $$ f(x)=\sqrt{-8-8 x} $$ Answer Attempt 1 out of 2 Answer Type: Interval

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UpStudy AI · Accepted Answer

To determine the domain of the function $$ f(x) = \sqrt{-8 - 8x} $$, we need to ensure that the expression inside the square root is non-negative (since the square root of a negative number is not a real number).

### Step-by-Step Solution:

1. **Set the radicand (the expression inside the square root) greater than or equal to zero:**
   $$
   -8 - 8x \geq 0
   $$

2. **Solve for $$ x $$:**
   $$
   -8x \geq 8
   $$
   
   $$
   x \leq -1
   $$
   (Note: When dividing or multiplying by a negative number, the inequality sign flips.)

3. **Interpret the inequality:**
   - The function $$ f(x) $$ is defined for all real numbers $$ x $$ that are less than or equal to $$-1$$.

### Domain in Interval Notation:
$$
(-\infty, -1]
$$

**Final Answer:**

$$
\boxed{\,(-\infty,\ -1\,]\,}
$$
The domain of $$ f(x) = \sqrt{-8 - 8x} $$ is all real numbers less than or equal to $$-1$$, which is written as $$ (-\infty, -1] $$.

Find the domain of .

Answer Attempt 1 out of 2
Answer Type: Interval

Upstudy AI Solution

Answer

Solution

Step-by-Step Solution:

Domain in Interval Notation:

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Find the domain of . Answer Attempt 1 out of 2 Answer Type: Interval