Is the function one-to-one? Is the function $f: \mathbb R+ \to\mathbb R \\$ defined as $f(x) = \sqrt{x} + x + 2$ one-to-one?
I'm pretty sure the function is one to one but when I try to solve $f(x) = f(y)$ to $x = y$  I get suck at $\sqrt{x} + x = \sqrt{y} + y$ and don't know where to continue.
Thanks

From your last expression, we have 
$$\sqrt{x} - \sqrt{y} = y - x = -(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})$$
If $x \neq y$, does that lead to a contradiction?
