The discussion focuses on determining why the function fr(x) = 1.5/sin(x) has an inverse function, highlighting the need to identify intervals where the function is one-to-one. It emphasizes that a function must be strictly increasing or decreasing to have an inverse, and suggests graphing y = 1.5 csc(x) over a larger interval to better understand its domain and range. The principal domain is clarified as [-π/2, 0) U (0, π/2], while the range is (-∞, -1.5) U (1.5, ∞). The inverse function's domain and range are discussed, concluding that the image set is (0, 1/2π] and the domain is (1.5, ∞). Understanding these properties is essential for explaining the existence of the inverse function.