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**mr fantastic** Let $\displaystyle g(x) = \frac{x - 2}{x + 6} = \frac{x + 6 - 8}{x + 6} = 1 - \frac{8}{x + 6}$. g has a range of (-oo, 1) U (1, +oo).

Let $\displaystyle f(x) = \sqrt{x}$. The maximal domain of f is [0, +oo).

Therefore $\displaystyle y = \sqrt{\frac{x-2}{x+6}} = f(g(x))$ is only defined when the range of g is resticted to lie in [0, oo).

Under this restriction, the 'maximal input' for f will be [0, 1) U (1, +oo) and so the 'maximal output' of f will be [0, 1) U (1, +oo).

Therefore the range of $\displaystyle y = \sqrt{x-2}{x+6}$ is [0, 1) U (1, +oo).