Question

If the domain of the square root function f(x) is x less-than-or-equal-to 7, which statement must be true?
7 is subtracted from the x-term inside the radical.
The radical is multiplied by a negative number.
7 is added to the radical term.
The x-term inside the radical has a negative coefficient.

Answer 1

"The x-term inside the radical has a negative coefficient."

Reason: For a square root sqrt(ax + b) to be defined only when x ≤ 7, the linear coefficient a must be negative so ax + b ≥ 0 gives x ≤ -b/a = 7. The other choices either give the wrong inequality direction or don't affect the domain.