Question

If c(x)= }{x-2} " align="absmiddle" class="latex-formula"> 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

$\bf \begin{cases} c(x)=\cfrac{5}{x-2}\\\\ d(x)=x+3\\ ----------\\ (cd)(x)\implies c(x)\cdot d(x) \end{cases} \\\\\\ c(x)\cdot d(x)\implies \left( \cfrac{5}{x-2}\right)(x+3)\implies \cfrac{5(x+3)}{x-2}$

now, for a fraction, if its denominator ever becomes 0, the fraction becomes undefined, because it'd be a division by 0.

when does that happen?  let's zero out the denominator to check,

x - 2 = 0, thus x = 2

so, if "x" ever becomes 2, the fractions goes kaput.

so, that domain is all real values except that one, that makes the fraction undefined.