Find domain and range of f(x, y)

Question

We consider the function

f(x, y)=1/sqrt(3-5x^2 - 7y^2)

a) Find the domain of f.

O (7/3)x2 + (5/3)y² > 1

O (5/3)2 + (7/3)² ≥ 1

O (5/3)z² + (7/3)y² > 1

O (5/3)z2 + (7/3)y² <1

O (5/3)z2 + (7/3)y² <1

O (7/3)x² + (5/3)y² < 1

b) Find the range of f

Answer 1

Part a) Domain is the set of all x's and y's that can be plugged into the equation.

In your problem, the 2 restrictions are:

1) Your denominator cannot be equal to 0.

2) What is under the square root cannot be negative.

Therefore, we can say:

3 - 5x² - 7y² > 0

We can add 5x²+7y² to both sides:

3>5x²+7y²

Then divide both sides by 3:

Final Answer: 1>(5/3)x²+(7/3)y²

Part b) Range is the possible numbers f(x,y) can be (or the possible numbers z can be).

Since it's a fraction is can be all possible numbers (except 0). However, since the denominator cannot be negative since it's under a square root, the options are all positive numbers.

Range= (0,∞)