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Ivan
3 years ago
15

Do anyone know how to solve this problem

Mathematics
1 answer:
sergey [27]3 years ago
3 0

Answer:

The domain is \boxed{D_f = [0, \infty)}.

Step-by-step explanation:

Let f(x) = \dfrac{\sqrt{2x}}{x+1}.

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:

x+1 \neq 0 \iff x \neq -1.

On the other hand, there's also a square root, whose argument can't be negative. This means that:

2x \geq 0 \iff x \geq 0.

So the domain is:

\boxed{D_f =\{x\in\mathbb{R}: x\geq 0 \textrm{ and } x \neq -1\} = [0, \infty)}.

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