9. $$ y=\frac{\sqrt{x-3}}{\sqrt{x-6}} \quad $$ Domain: $$ 1- $$

Question

UpStudy AI · Accepted Answer

To find the domain of the function $$ y = \frac{\sqrt{x-3}}{\sqrt{x-6}} $$, we need to determine the values of $$ x $$ for which the expression is defined.

1. **Square Root Conditions**: The square root function is defined only for non-negative values. Therefore, we need to ensure that both the numerator and the denominator are non-negative.

- For the numerator $$ \sqrt{x-3} $$:
     $$
     x - 3 \geq 0 \implies x \geq 3
     $$

- For the denominator $$ \sqrt{x-6} $$:
     $$
     x - 6 > 0 \implies x > 6
     $$
     (Note: The denominator cannot be zero, hence we use $$ > $$ instead of $$ \geq $$.)

2. **Combining Conditions**: The conditions we have are:
   - $$ x \geq 3 $$ from the numerator.
   - $$ x > 6 $$ from the denominator.

The more restrictive condition is $$ x > 6 $$.

3. **Conclusion**: Therefore, the domain of the function $$ y = \frac{\sqrt{x-3}}{\sqrt{x-6}} $$ is:
   $$
   \text{Domain: } (6, \infty)
   $$

In interval notation, the domain is $$ (6, \infty) $$.
Domain: $$ (6, \infty) $$

Domain:

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Pre Calculus Questions