Question

Domain Find the domain of the function.

$f\left(x\right)=\sqrt{x}+\sqrt{3-x}$

Short answer

The domain of the given function is $\left[0,3\right]$.

Step-by-step solution

– Domain of a function.

Domain of a function is the set of all possible input values.

– Given information.

The given function is:

$f\left(x\right)=\sqrt{x}+\sqrt{3-x}$

– Domain of the given function.

For$\sqrt{x}$to be defined, we must have $x\ge 0$.

For$\sqrt{3-x}$ to be defined, we must have$3-x\ge 0$ that is $3\ge x$.

So, the given function$f\left(x\right)$ is defined for all real values x such that $0\le x\le 3$.

Thus, the domain of the given function is $\left[0,3\right]$.