Question

If c(x)= 5/x-2 and d(x) = x + 3, what is the domain of (cd)(x)?

Answer 1

`(fg)(x)=f(x)\cdot g(x)\\\\\text{We have}\ c(x)=(5)/(x-2)\ \text{and}\ d(x)=x+3.\ \text{Substitute}\\\\(cd)(x)=(5)/(x-2)\cdot(x+3)=(5(x+3))/(x-2)\\\\\text{Domain:}\\\\\text{The denominator must be different than zero. Therefore}\\\\x-2\\eq0\to x\\eq2\\\\Answer:\ \text{Domain is the set of all real numbers except 2}\to D=\mathbb{R}-\{2\}`