Question

If c(x)=5/X-2 and d(x) = x + 3, 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

Answer:

all real values except x = 2

Step-by-step explanation:

$(c \times d)(x) = c(x) \times d(x) \\ = \frac{5}{x - 2} \times x + 3 \\ = \frac{5x + 15}{x - 2}$

Hence, the function is defined for all values except 2 ( 2 - 2 in the denominator becomes 0 and division by zero is undefined ). Hence,

Domain = R - { 2 } or all real numbers except 2.

Answer 2

Option B) all real values of x except x = 2

Step-by-step explanation:

We are given the following in the question:

$c(x) = \dfrac{5}{x-2}\\\\d(x) = x + 3$

First we will evaluate (cd)(x)

$(cd)(x) = \dfrac{5}{x-2}\times (x+3) = \dfrac{5(x+3)}{x-2}$

We have to find the domain of the resultant function.

The domain is all the possible values that x can take so that the function is defined.

Thus, the domain of (cd)(x) is

$x \in (-\infty,\infty)-\{2\}$

That is the domain is all real numbers except x = 2.

Thus, the correct answer is

Option B) all real values of x except x = 2

#LearnMore

Consider the real valued fun ction, F(x)= x-3/x^2-x-6 . Find the domain of f(x).​

https://brainly.in/question/11273947