Final answer:
The domain of the function is all real numbers except -4 and 4. The range of the function is all real numbers greater than or equal to 2.
Step-by-step explanation:
To find the domain of the function, we need to consider the values that x can take. In this case, the denominator cannot be equal to zero since it would result in division by zero. So, we need to find the values of x that make the denominator equal to zero. Solving for x in the equation √(16 - x²) = 0, we find that x = -4 and x = 4. Therefore, the domain of the function is all real numbers except -4 and 4, written in interval notation as (-∞, -4) U (-4, 4) U (4, ∞).
To find the range of the function, we need to consider the values that y (or f(x)) can take. The square root function only gives non-negative results, so the numerator must also be greater than or equal to zero. Solving for x in the inequality x - 2 ≥ 0, we find that x ≥ 2. Therefore, the range of the function is all real numbers greater than or equal to 2, written in interval notation as [2, ∞).