if $c(x)=\frac{5}{x - 2}$ and $d(x)=x + 3$, what is the domain of $(cd)(x)$?\nall real values of $x$\nall…

if $c(x)=\frac{5}{x - 2}$ and $d(x)=x + 3$, what is the domain of $(cd)(x)$?\nall real values of $x$\nall real values of $x$ except $x = 2$\nall real values of $x$ except $x=-3$\nall real values of $x$ except $x = 2$ and $x=-3$

if $c(x)=\frac{5}{x - 2}$ and $d(x)=x + 3$, what is the domain of $(cd)(x)$?\nall real values of $x$\nall real values of $x$ except $x = 2$\nall real values of $x$ except $x=-3$\nall real values of $x$ except $x = 2$ and $x=-3$

Answer

Answer:

B. all real values of x except x = 2

Explanation:

Step1: Define the product function

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

Step2: Identify domain - restriction condition

The denominator of a fraction cannot be zero.

Step3: Solve for the restricted value

Set $x-2=0$. Then $x = 2$. So the domain of $(cd)(x)$ is all real values of $x$ except $x = 2$.