The number of points of discontinuity of the rational function f(x)= x^2-3 x+2 4 x-x^3

Step-by-step solution

The function is defined as f(x) = x^2 - 3x + 2 4x - x^3 . Factorizing the numerator and the denominator: Numerator: x^2 - 3x + 2 = (x - 1)(x - 2) Denominator: 4x - x^3 = x(4 - x^2) = x(2 - x)(2 + x) = -x(x - 2)(x + 2) Thus, f(x) = (x - 1)(x - 2) -x(x - 2)(x + 2) . The function is undefined where the denominator is zero, which occurs at x = 0 , x = 2 , and x = -2 . Simplifying the expression for x 2 : f(x) = x - 1 -x(x + 2) for x 2 . At x = 0 and x = -2 , the denominator is zero while the numerator is non-zero, so t