Question

Domain and range of √16-x²-4y²/x²-y².

A) (-4, 4) for both domain and range
B) (-[infinity], -4) ∪ (4, [infinity]) for the domain, (-[infinity], -1) ∪ (1, [infinity]) for the range
C) (-4, 4) for the domain, (-[infinity], [infinity]) for the range
D) (-[infinity], -4]∪ [4, [infinity]) for the domain, (-[infinity], [infinity]) for the range

Answer 1

The domain of the expression is (-4, 4) and the range is (-[infinity], [infinity]).

Step-by-step explanation:

The domain and range of the given expression √(16 - x² - 4y²)/(x² - y²) can be determined by analyzing the restrictions and possible values of the variables.

The expression inside the square root, 16 - x² - 4y², must be greater than or equal to 0 for the square root to be defined. Solving this inequality, we get x² + 4y² ≤ 16.

Since the denominator, x² - y², must not be equal to 0, we exclude the values of x and y that make this happen.

The correct option is C) (-4, 4) for the domain and (-[infinity], [infinity]) for the range.