Determine the domain of the following functions. Determine where the function is continuous. If it is not continuous, state why. a) f(x)= 3x^2 -5x +7 b) f(x) = \frac{x + 4}{ {x}…

Question

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

a) f(x)= 3x^2 -5x +7

b)

`f(x) = \frac{x + 4}{ {x}^(2) - x}`
c)

`f(x) = (x)/( √(x - 2) )`
​

Answer 1

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.