Splitting up curves The unit circle x² + y² = 1  consists of four one-to-one functions, ƒ₁ (x), ƒ₂(x) , ƒ₃(x), and ƒ₄ (x)  (see figure)<IMAGE>.


b. Find the inverse of each function and write it as y= ƒ⁻¹ (x)

Verified step by step guidance

1. Step 1: Understand the unit circle equation x^2 + y^2 = 1, which represents a circle centered at the origin with a radius of 1.
2. Step 2: Recognize that the unit circle can be divided into four segments, each representing a one-to-one function. These segments correspond to the four quadrants of the circle.
3. Step 3: Identify the four functions: f₁(x) for the top right quadrant, f₂(x) for the top left quadrant, f₃(x) for the bottom left quadrant, and f₄(x) for the bottom right quadrant.
4. Step 4: For each function, express y in terms of x. For example, for f₁(x), y = sqrt(1 - x^2) since it represents the top half of the circle where y is positive.
5. Step 5: Find the inverse of each function by solving for x in terms of y. For instance, for f₁(x), the inverse would be x = sqrt(1 - y^2), and express it as y = f⁻¹(x).