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…

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

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 - avoid division by zero

The denominator of a fraction cannot be zero. Set $x-2\neq0$. Solving $x - 2\neq0$ gives $x\neq2$.

Answer:

all real values of x except x = 2