Answer
f∘g $ \frac {1}{\sqrt{x^2 - 4x}}$ Domain: (-∞, 0) U (4, ∞)
g∘f $\frac{1}{x} - \frac{4}{\sqrt x}$ Domain: (0, ∞)
f∘f $\sqrt x$ Domain: (0, ∞)
g∘g $x^4 - 8x^3 + 12x^2 + 16x$ Domain: (- ∞, ∞)
Work Step by Step
$f(x) = \frac{1}{\sqrt x}$
$g(x) = x^2 - 4x $
f∘g $f(x^2 - 4x) = \frac {1}{\sqrt{x^2 - 4x}}$ Domain: (-∞, 0) U (4, ∞)
g∘f $g(\frac{1}{\sqrt x}) = (\frac{1}{\sqrt x})^{2} - 4(\frac{1}{\sqrt x})$
=$\frac{1}{x} - \frac{4}{\sqrt x}$ Domain: (0, ∞)
f∘f $f(\frac{1}{\sqrt x}) = \frac{1}{\frac{1}{\sqrt x}}$
=$\sqrt x$ Domain: (0, ∞)
g∘g $g(x^2 - 4x) = (x^2 - 4x)^2 - 4(x^2 - 4x) $
=$x^4 - 8x^3 + 12x^2 + 16x$ Domain: (- ∞, ∞)