KCET · Maths · Functions
Domain \(\cos ^{-1}[x]\) is, where [] denotes a greatest integer function
- A \((-1,2]\)
- B \((-1,2)\)
- C \([-1,2]\)
- D \([-1,2)\)
Answer & Solution
Correct Answer
(D) \([-1,2)\)
Step-by-step Solution
Detailed explanation
Let \(y=\cos ^{-1}[x]\)
We know, for \(\cos ^{-1} x\)
\[
\Rightarrow \quad-1 \leq x \leq 1
\]
Therefore, for \(\cos ^{-1}[x]\)
\[
\Rightarrow \quad-1 \leq[x] \leq 1 \Rightarrow-1 \leq x < 2 \Rightarrow x \in[-1,2)
\]
We know, for \(\cos ^{-1} x\)
\[
\Rightarrow \quad-1 \leq x \leq 1
\]
Therefore, for \(\cos ^{-1}[x]\)
\[
\Rightarrow \quad-1 \leq[x] \leq 1 \Rightarrow-1 \leq x < 2 \Rightarrow x \in[-1,2)
\]
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