suppose f(x)=x+4/x^2-4x-5 and g(x)= rad 3-x. algebraically determine the domain of f(x)/g(x)
the domain of rational functions is all real numbers except where the denominator is zero
since
x^2-4x-5=0 when x = -1 or 5
√(3-x) is undefined when 3-x < 0, its domain is x <= 3
so, the domain of f/g is (-∞,-1)U(-1,3) because anywhere else either f or g or f/g is undefined.