Question

What is the domain of (cd)(x)?

all real values of x
all real values of x except x = 2
all real values of x except x = –3
all real values of x except x = 2 and x = –3

Answer 1

Only option B is correct, i.e. all real values of x except x = 2.

Explanation:

Given the functions are C(x) = 5/(x-2) and D(x) = (x+3)

Finding (C·D)(x) :-

(C·D)(x) = C(x) * D(x)

(C·D)(x) = 5/(x-2) * (x+3)

(C·D)(x) = 5(x+3) / (x-2)

(C·D)(x) = (5x+15) / (x-2)

Let y(x) = (C·D)(x) = (5x+15) / (x-2)

According to definition of functions, the rational functions are defined for all Real values except the one at which denominator is zero.

It means domain will be all Real values except (x-2)≠0 or x≠2.

Hence, only option B is correct, i.e. all real values of x except x = 2.