Question

Determine the domain of the following functions. Determine where the function is continuous. If it is not continuous, state why.

Answer 1

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.