Find the domain of the function. $$ f(x)=\frac{1}{\sqrt{x-8}} $$ The domain of $$ f(x) $$ is $$ \square $$. (Type your answer in interval notation.)

Question

UpStudy AI · Accepted Answer

To find the domain of the function $$ f(x) = \frac{1}{\sqrt{x-8}} $$, we need to determine the values of $$ x $$ for which the function is defined.

1. **Identify the restrictions**: 
   - The expression under the square root, $$ x - 8 $$, must be greater than zero because the square root of a negative number is not defined in the real number system, and the denominator cannot be zero.

2. **Set up the inequality**:
   $$
   x - 8 > 0
   $$

3. **Solve the inequality**:
   $$
   x > 8
   $$

4. **Express the domain in interval notation**:
   The values of $$ x $$ that satisfy this inequality are all real numbers greater than 8. Therefore, the domain of $$ f(x) $$ is:
   $$
   (8, \infty)
   $$

Thus, the domain of $$ f(x) $$ is $$ (8, \infty) $$.
The domain of $$ f(x) $$ is $$ (8, \infty) $$.

Find the domain of the function. \( f(x)=\frac{1}{\sqrt{x-8}} \) The domain of \( f(x) \) is \( \square \). (Type your answer in interval notation.)

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Algebra Questions