Davey Rodriguez
08/30/2023 · High School
The domain of \( g(x)=\sqrt{2-x} \) is \( \square \). (Type your answer in interval notation. Simplit
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ify your argument to make it as concise as possible.
To find the domain of \( g(x)=\sqrt{2-x} \), we need to ensure that the expression inside the square root is non-negative, since the square root of a negative number is not defined in the real number system.
So, we set \( 2-x \geq 0 \) and solve for \( x \):
\[
\begin{align*}
2-x &\geq 0 \\
-x &\geq -2 \\
x &\leq 2
\end{align*}
\]
Therefore, the domain of \( g(x) \) is \( (-\infty, 2] \).
The domain of \( g(x)=\sqrt{2-x} \) is \( (-\infty, 2] \).
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The domain of \( g(x)=\sqrt{2-x} \) is \( (-\infty, 2] \).
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