f(x) = 1 / squarroot(x)
g(x) = x^2 - 4x
how do i begin?
$\displaystyle (\tfrac{f}{g})(x) = \frac{\frac{1}{\sqrt{x}}}{x^2 - 4x} = \frac{1}{\sqrt{x} \left(x^2 - 4x\right)} = \frac{1}{x\sqrt{x}(x-4)}$
There's an extra restriction here. Remember, can't have a division by 0.
$\displaystyle (f \circ g)(x) = f(g(x)) = f(x^2 + 4x) = \frac{1}{\sqrt{x^2 + 4x}}$
Just like earlier analysis, we can't have a division by 0 nor a square root of a negative number. So, our domain is restricted to values such that: $\displaystyle x^2 + 4x > 0$