Question

Which function has a restricted domain?

A. g(x)=(3x)¹/⁵ - 4
B. k(x) = (-x+3)¹/²
C. g(x) = -(x+8)³
D. h(x) =4(x)² - 5

Answer 1

Option B, k(x) = (-x+3)¹/², has a restricted domain where x ≤ 3.

Step-by-step explanation:

The function that has a restricted domain is option B, k(x) = (-x+3)¹/².

A restricted domain means that there are certain values of x for which the function is not defined. In this case, the function k(x) is not defined for values of x that would result in taking the square root of a negative number. The square root function is only defined for non-negative numbers, so the domain of k(x) is restricted to values where -x+3 is greater than or equal to 0.

For example, if we solve -x+3 ≥ 0, we find that x ≤ 3. So the domain of k(x) is x ≤ 3.