Question

Find (f-g)(x). What is the domain of f/g f(x)=2x-5 g(x)=2-x

Answer 1

$f(x)=2x-5 , \ \ \ \ g(x)=2-x \\\\(f-g)(x)=f(x)-g(x) = 2x-5 -(2-x)=2x-5-2+x = 3x+5 \\\\\\ domain : \frac{f}{g}=\frac{2x-5}{2-x}\\\\2-x\neq 0 \\ \\x\neq 2 \\ \\D=R\setminus \left \{ 2 \right \}$