Answer:
- D: [-2, 6) ∪ (6, ∞)
- R: (-∞, 8]
Step-by-step explanation:
Domain
The argument of the square root function must be non-negative, so ...
... x+2 ≥ 0
... x ≥ -2
The denominator cannot be zero, so there is a disallowed value of x at ...
... x/2 -3 = 0
... x/2 = 3
... x = 6 . . . . . . . . . excluded from the domain
Range
The value of the expression is 8 for x=-2. As x approaches 6, the value of y approaches -∞.
Because the denominator is squared (has an even exponent), the sign does not change as x crosses 6, so function values increase from -∞ toward the horizontal asymptote at y=8.
Thus the range is (-∞, 8].
