Given f(x) = sqrt(2−x) and g(x) = x2+5, find fog and gof.

The composite function $f \circ g(x)$ is defined as $f(g(x))$. We substitute $g(x)$ into $f(x)$.

$$f(g(x)) = f(x^2 + 5)$$

Now, replace $x$ in $f(x)$ with $(x^2 + 5)$:

$$f(x^2 + 5) = \sqrt{2 - (x^2 + 5)}$$

Simplify the expression inside the square root:

$$f(x^2 + 5) = \sqrt{2 - x^2 - 5}$$ $$f(x^2 + 5) = \sqrt{-x^2 - 3}$$

The result for $f \circ g(x)$ is $\boxed{\sqrt{-x^2 - 3}}$.

The composite function $g \circ f(x)$ is defined as $g(f(x))$. We substitute $f(x)$ into $g(x)$.

$$g(f(x)) = g(\sqrt{2-x})$$

Now, replace $x$ in $g(x)$ with $(\sqrt{2-x})$:

$$g(\sqrt{2-x}) = (\sqrt{2-x})^2 + 5$$

Simplify the expression. Note that $(\sqrt{A})^2 = A$ for $A \ge 0$:

$$g(\sqrt{2-x}) = (2-x) + 5$$ $$g(\sqrt{2-x}) = 7-x$$

The result for $g \circ f(x)$ is $\boxed{7-x}$.