Question

The domain of cosine ceiling function i.e. domain of $co{s}^{-1}[x]$ is

• A. $[-2,1]$
• B. $[-2,1)$
• C. $(-2,1]$
• D. None of these

Answer 1

Answer: (C)

Let $f(x)=co{s}^{-1}[x]$
Now, domain of $g(x)=co{s}^{-1}x$ is the set
$\{x:-1\le x\le 1\}=[-1,1]$
$\therefore$ Domain of given function is
$\{x:-1\le [x]\le 1=\{x:[x]=-1,0,1\}$
$\therefore$ $[x]=\{\begin{array}{ll}-1& \text{if }-2<x\le -1\\ 0& \text{if }-1<x\le 0\\ 1& \text{if }0<x\le 1\end{array}$
Hence, required domain of $co{s}^{-1}[x]$ is $(-2,1]$