if $c(x)=\frac{5}{x - 2}$ and $d(x)=x + 3$, what is the domain of $(cd)(x)$?\no all real values of $x$\no…

if $c(x)=\frac{5}{x - 2}$ and $d(x)=x + 3$, what is the domain of $(cd)(x)$?\no all real values of $x$\no all real values of $x$ except $x = 2$\no all real values of $x$ except $x=-3$\no all 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 $(cd)(x)$?\no all real values of $x$\no all real values of $x$ except $x = 2$\no all real values of $x$ except $x=-3$\no all real values of $x$ except $x = 2$ and $x=-3$

Answer

Explanation:

Step1: Find the product function

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

Step2: Determine the domain - undefined values

The function is undefined when the denominator is 0. Set $x-2=0$, we get $x = 2$.

Answer:

all real values of x except x = 2