Answer:
Explanation:
The domain of a function is the set of values of the independent variable, x, for which the result of the function, y, is defined. To find the domain of the function, we need to determine what values of x will result in a defined value of y.
In this case, there are two things we need to check for: division by zero, and taking the square root of a negative number.
First, we need to check if there are any values of x that would lead to dividing by zero in the function. This would happen if x-7 is equal to zero, so we need to find the values of x for which x-7=0. Adding 7 to both sides, we get x=7. Since the function is already defined at x=7, there is no problem with dividing by zero.
Next, we need to check if there are any values of x that would lead to taking the square root of a negative number in the function. In general, the square root of a number is only defined for non-negative values of the number. So in this case, we need to find the values of x for which 10-x is negative. Subtracting 10 from both sides, we get x<10. Since the function is already defined for x<7, there is no problem with taking the square root of a negative number.
Putting all of this together, we get the following domain for the function:
Dom(y) = x
This is the set of values of x for which the function y is defined.