TS EAMCET · Maths · Functions
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
- A \((-1,3)\)
- B \([-1,3)\)
- C \((-1,3]\)
- D \([-1,3)\)
Answer & Solution
Correct Answer
(A) \((-1,3)\)
Step-by-step Solution
Detailed explanation
Given that, \[ \begin{aligned} & \qquad f(x)=\left\{\begin{array}{l} {[x] \text { if }-3 < x \leq-1} \\ |x| \text { if }-1 < x < 1 \\ |[x]| \text { if } 1 \leq x < 3 \end{array}\right. \\ & \text { When }-3 < x \leq-1, f(x)=[x] \\ & \Rightarrow \quad f(x) < 0 \end{aligned} \]
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