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If $f(x)=\left\{\begin{array}{ll}{[x]} & \text { if }-3 < x \leq-1 \\ |x| & \text { if }-1 < x < 1 \\ |[x]| & \text { if } 1 \leq x < 3\end{array}\right.$ then the set $(x: f(x) \geq 0)$ is equal to
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2298 Upvotes
Verified Answer
The correct answer is:
$(-1,3)$
Given that,
$$
\begin{aligned}
& \qquad f(x)=\left\{\begin{array}{l}
{[x] \text { if }-3 < x \leq-1} \\
|x| \text { if }-1 < x < 1 \\
|[x]| \text { if } 1 \leq x < 3
\end{array}\right. \\
& \text { When }-3 < x \leq-1, f(x)=[x] \\
& \Rightarrow \quad f(x) < 0
\end{aligned}
$$
$$
\begin{aligned}
& \qquad f(x)=\left\{\begin{array}{l}
{[x] \text { if }-3 < x \leq-1} \\
|x| \text { if }-1 < x < 1 \\
|[x]| \text { if } 1 \leq x < 3
\end{array}\right. \\
& \text { When }-3 < x \leq-1, f(x)=[x] \\
& \Rightarrow \quad f(x) < 0
\end{aligned}
$$
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