1. The problem is to simplify and analyze the function $$y=\frac{\sqrt{x}-1}{x+1}$$. 2. The formula involves a square root in the numerator and a linear expression in the denominator. 3. Important rules: - The domain must exclude values that make the denominator zero. - The expression under the square root must be non-negative for real values. 4. Domain analysis: - Denominator: $x+1 \neq 0 \Rightarrow x \neq -1$. - Radicand: $x \geq 0$. 5. Therefore, the domain is $[0, \infty)$ excluding $x=-1$ which is outside this interval, so domain is $[0, \infty)$. 6. Simplify the expression if possible: - No common factors to cancel. 7. Evaluate at some points to understand behavior: - At $x=0$: $y=\frac{\sqrt{0}-1}{0+1} = \frac{0-1}{1} = -1$. - At $x=1$: $y=\frac{1-1}{1+1} = 0$. 8. The function is continuous on $[0, \infty)$. Final answer: The function is $$y=\frac{\sqrt{x}-1}{x+1}$$ with domain $x \geq 0$ and $x \neq -1$ (which is irrelevant here).