determine y as a function of x

Question

Does the equation x^2 - y^2 = 1 determine y as a function of x?

Answer 1

The Equation is x^2 - y^2 = 1

Subtract  "x^2" on both sides

x^2 - y^2 - x^2 = 1 - x^2

0 - y^2 = 1 - x^2

Multiply with "-1" on both sides

-1 (-y^2) = -1(1 - x^2)

y^2 = -1 + x^2

y^2 = x^2 - 1

Apply "sqrt" on both sides

(y^2)^1/2 = (1 - x^2)^1/2

y = (1 - x^2)^1/2