Question

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

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

Answer 1

Answer: (C)

Let $f(x) = cos^{-1}[x]$
Now, domain of $g(x) = cos^{-1} x$ 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{cases} -1 & \quad \text{if } -2 < x \le -1 \\ 0 & \quad \text{if } -1 < x \le 0 \\ 1 & \quad \text{if } 0 < x \le 1 \end{cases} $
Hence, required domain of $cos^{-1} [x]$ is $(-2, 1]$