Question

If f(x)= x-3/x and g(x)= 5x-3, what is the domain of (f•g)(x)

Answer 1

`f(x)=(x-3)/(x),\ D_f:x\\eq0\\\\g(x)=5x-3,\ D_g=\mathbb{R}\\\\(f\cdot g)(x)=f(x)\cdot g(x)\\\\(f\cdot g)(x)=(x-3)/(x)\cdot(5x-3)=((x-3)(5x-3))/(x)\\\\D_((f\cdot g))=D_f`

Answer: The domain of (f•g)(x) is all real numbers except for 0

`D=\mathbb{R}-\{0\}`