The domain of the real valued function f(x) = | vedclass

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(A) For the function $f(x) = \frac{\sqrt{2-x} + \sqrt{1+x}}{\sqrt{x+3}}$ to be defined,the expressions under the square roots must be non-negative,and

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$[-1, 2]$

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(A) For the function $f(x) = \frac{\sqrt{2-x} + \sqrt{1+x}}{\sqrt{x+3}}$ to be defined,the expressions under the square roots must be non-negative,and the denominator must not be zero.$1$. For $\sqrt{2-x}$,we require $2-x \geq 0$,which implies $x \leq 2$.$2$. For $\sqrt{1+x}$,we require $1+x \geq 0$,which implies $x \geq -1$.$3$. For $\sqrt{x+3}$ in the denominator,we require $x+3 > 0$,which implies $x > -3$.Combining these conditions: $x \leq 2$,$x \geq -1$,and $x > -3$.The intersection of these intervals is $[-1, 2]$.

The domain of the real valued function $f(x) = \frac{\sqrt{2-x} + \sqrt{1+x}}{\sqrt{x+3}}$ is

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