Answer
See below.
Work Step by Step
a) $(f+g)(x)=f(x)+g(x)=x^2-5x+1-4x-7=x^2-9x-6$. This function is defined for all real numbers, thus its domain is all the real numbers.
b) $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{x^2-5x+1}{-4x-7}$. This function is defined for all real numbers apart from when the denominator is $0$ (which is when $-4x-7=0$, thus $-4x=7$, thus $x=-1.75$. Its domain is all the real numbers apart from $-1.75$.
