Question

Let f(x)=3x and g(x)=x^2+5. Perform function operation g(x)/f(x). State the domain.

Answer 1

We have that

f(x)=3x
g(x)=x²+5
g(x)/f(x)=[x²+5]/[3x]

that new function will exist for all real numbers except the value of zero, value for which it becomes indefinite

the domain is the interval (-∞,0) U (0,∞)

using a graph tool
see the attached figure