Question

If the domain of the square root function f(x) is x ≤ 7, which statement must be true?

a) 7 is subtracted from the x-term inside the radical.
b) The radical is multiplied by a negative number.
c) 7 is added to the radical term.
d) The x-term inside the radical has a negative coefficient.

Answer 1

Statement c) 7 is added to the radical term must be true.The fact that the domain of the square root function is x ≤ 7 implies that the x-term inside the radical has a negative coefficient, aligning the function with the given domain restriction.

Step-by-step explanation:

To determine which statement must be true given the domain of the square root function is x ≤ 7, we need to understand how the domain affects the function. Since the domain is x ≤ 7, it means that only values of x that are less than or equal to 7 are allowed.

This is because the square root function is not defined for negative values of x. Therefore, statement c) 7 is added to the radical term must be true, as adding 7 to x ensures that x will always be a non-negative value.

Therefore the correct answer is c) 7 is added to the radical term.