(g/f)(x)
= g(x) / f(x)
= (x^2 + 3) / (5x-4)
the denominator = 0 when 5x-4 = 0
this occurs when x = 4/5
the function is undefined when the denominator is equal to 0
the domain is therefore all real values of x except when x = 4/5
the graph of this equation looks like this:
if you draw a vertical line at x = 4/5, you will see that the graph of the function approaches that line but never touches it. that means that the line x = 4/5 is an asymptote of the function which also means that that the function is undefined at x = 4/5.
