Question

Define a rational function with the given domain: Domain = x is a real number except -2 and 3.

A) f(x) = (x + 2)(x - 3) / (x + 2)
B) f(x) = (x - 2)(x + 3) / (x - 2)
C) f(x) = (x - 2)(x - 3) / (x + 3)
D) f(x) = (x + 2)(x + 3) / (x - 3)

Answer 1

The rational function with the given domain x is f(x) = (x - 2)(x + 3) / (x - 2).

Step-by-step explanation:

A rational function is defined as a function that can be expressed as a fraction of two polynomial functions. To define a rational function with the given domain x , we need to choose an expression that eliminates -2 and 3 from the denominator.

Looking at the options, option B, f(x) = (x - 2)(x + 3) / (x - 2), satisfies this condition. In this option, x = -2 is excluded from the domain because the factor (x - 2) cancels out in the numerator and denominator. Similarly, x = 3 is excluded because it would make the denominator equal to zero. Therefore, option B is the correct choice.