Question

Determine if the equation x^2 + 3y^2= 3 defines y as a function of x

Answer 1

y is NOT a function.

Explanation:

The equation given to us is:

x² + 3y² = 3

Rearrange the equation:

3y² = 3 - x²

y² = (3 - x²)/3

y² = 1 - (x²)/3

y = ±√(1 - x²/3)

For any equation to be a function, there should be only one output for one input. Which means that for any value of x, there should be only one value of y. However, in this equation, as the underroot gives two values of any terms under it, it shows that if we put any value of x, we'll get 2 values of y. Therefore, y is not a function.