To determine the domain of the function $f(x) = \frac{\sqrt{x}}{x - 70}$, we need to identify the values of $x$ for which the function is defined.

There are two key conditions we must consider:

1. The expression inside the square root, $\sqrt{x}$, must be non-negative because the square root of a negative number is undefined in the real number system. So, $x \geq 0$.
2. The denominator $x - 70$ cannot be zero, because division by zero is undefined. Therefore, $x \neq 70$.

Summary:

• From condition 1: $x \geq 0$.
• From condition 2: $x \neq 70$.

Thus, the domain of the function is $x \in [0, 70) \cup (70, \infty)$.

In interval notation, the domain is:

$[0, 70) \cup (70, \infty)$

Would you like more details or have further questions? Here are some related questions you might find interesting:

1. How do square roots impact the domain of a function?
2. Why is $x \neq 70$ in this case?
3. Can the function be defined for negative values of $x$?
4. What happens to the function as $x$ approaches 70?
5. How do you find the domain of rational functions in general?

Tip: When dealing with square roots, always ensure that the expression inside the square root is non-negative!