Question

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

Answer 1

$f(x)=\dfrac{x-3}{x},\ D_f:x\neq0\\\\g(x)=5x-3,\ D_g=\mathbb{R}\\\\(f\cdot g)(x)=f(x)\cdot g(x)\\\\(f\cdot g)(x)=\dfrac{x-3}{x}\cdot(5x-3)=\dfrac{(x-3)(5x-3)}{x}\\\\D_{(f\cdot g)}=D_f$

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

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