You have the equation correct, namely f(x) = √(1 - x^{2}). What you need to do is specify the desired domain. The function f(x) restricted to the domain [0, 1] will yield the unit circle in quadrant 1.

Technically, f(x) = 1/4 * (|x|/x + 1) * (1 - |x - 1|/(x - 1)) * √(1 - x^{2}) will yield f(x) = 0 for x ∈ (-∞, 0) ∪ (1, ∞) and will yield f(x) = √(1 - x^{2}) for x ∈ (0, 1). It will be undefined for x = 0 or x = 1 but at least it doesn't require a domain restriction.

Henry D.

I don't understand the derivation of the equation07/23/21

Jacob C.

07/24/21

Henry D.

Can you please tell me how you got the equation: f(x) = 1/4 * (|x|/x + 1) * (1 - |x - 1|/(x - 1)) * √(1 - x2)07/23/21