Answer:
The domain is [tex]\boxed{D_f = [0, \infty)}[/tex].
Step-by-step explanation:
Let [tex]f(x) = \dfrac{\sqrt{2x}}{x+1}[/tex].
Since we have a fraction, we need to make sure that its denominator isn't zero, since division by zero isn't defined. This means that:
[tex]x+1 \neq 0 \iff x \neq -1.[/tex]
On the other hand, there's also a square root, whose argument can't be negative. This means that:
[tex]2x \geq 0 \iff x \geq 0.[/tex]
So the domain is:
[tex]\boxed{D_f =\{x\in\mathbb{R}: x\geq 0 \textrm{ and } x \neq -1\} = [0, \infty)}.[/tex]
