Answer:
Step-by-step explanation:
a) This function is a quadratic / polynomial. Alll polynomials are defined for all real numbers. The domain is (-∞, ∞).
b) this function's denominator is x(x-1), which is zero at x = 0 and at x = 1. Since we cannot divide by zero, neither 0 nor 1 is part of the domain. Expressed in positive terms, the domain is (-∞, 0) ∪ (0, 1) ∪ (1, ∞).
c) The domain of the square root function is [0, ∞). Given that the argument of the square root function in c) is x - 2, we find the domain by writing and solving the inequality x-2 > 0. This comes out to x > 2 or (2, ∞)
Continuity: (a) This function is continuous for all x.
(b) This function is continuous only for (-∞, 0) ∪ (0, 1) ∪ (1, ∞).
(c) This function is continuous only for x > 2.
