I'll give brainliest! y=-( (sqrt(x+2)) /(x/2-3) )^2 + 8 find the domain and range

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].