Question

f(x)=x^2-2x-15 g(x)=x+3 domain of f/g(x)

Answer 1

f(x)=x²-2x-15=(x-5)(x+3); g(x)=x+3.

f/g(x)=x-5 when x≠-3. So the domain of f/g is all x except x=3, that is, {(-∞,-3),(-3,∞)}.

x-5 is a straight line with y-intercept (0,-5) and x-intercept (5,0).

But the line is discontinuous because of a hole at (-3,-8).