1. The problem is to analyze the function $$f(x) = \frac{x^3 - 3 \sin x}{1 + \tan x}$$ and also consider the function $$f(x) = \sqrt{x}$$. 2. For the first function, we want to understand its behavior, domain, and possibly simplify or analyze it. 3. The formula for the function is given explicitly: $$f(x) = \frac{x^3 - 3 \sin x}{1 + \tan x}$$. 4. Important rules: - The denominator $$1 + \tan x$$ must not be zero, so $$\tan x \neq -1$$. - The sine and tangent functions are periodic and have specific domains. 5. For the second function, $$f(x) = \sqrt{x}$$, the domain is $$x \geq 0$$ because the square root is defined for non-negative numbers. 6. Since the user did not request a graph, we provide the function expressions and domain considerations. Final answers: - For $$f(x) = \frac{x^3 - 3 \sin x}{1 + \tan x}$$, domain excludes points where $$1 + \tan x = 0$$. - For $$f(x) = \sqrt{x}$$, domain is $$x \geq 0$$.