Question

For what values of the variable does each of the following expressions make sense? We call the set of this values the domain of the expression. sqaure root of -(6-x)

Answer 1

The square root of a number is only defined for non-negative numbers, since the square root of a negative number is not a real number.

For the expression sqaure root of -(6-x) to make sense mathematically, the expression inside the square root must be non-negative.

So, we need to find the values of x that make -(6-x) non-negative.

-(6-x) is non-negative when -(6-x) ≥ 0

Simplifying this inequality, we get 6-x ≤ 0

x ≤ 6

So, for x ≤ 6, the expression sqaure root of -(6-x) is defined and makes sense mathematically. This is the domain of the expression.

In summary, the domain of the expression sqaure root of -(6-x) is x ≤ 6.