Question

Domain of $cos^{-1} [x]$, where $[. ]$ denotes a greatest integer function

• A. $(-1, 2]$
• B. $[-1,2]$
• C. $(-1, 2)$
• D. $[-1, 2)$

Answer 1

Answer: (D)

$[-1, 2)$

Answer 2

The greatest integer function [x] takes any real number x and rounds it down to the nearest integer.
The range of the greatest integer function is the set of all integers.
The domain of the inverse cosine function, $\cos^{-1}(x)$, is [-1, 1], where x is a real number.
To find the domain of $\cos^{-1}[x]$, we need to determine the values of x for which [x] lies within the range of [-1, 1].
Since the range of [x] is the set of all integers, we need to find the integers that lie within the range of [-1, 1].
The integers that lie within the range of [-1, 1] are -1, 0, and 1.
Therefore, the domain of $\cos^{-1}[x]$ is the set of values for which [x] is equal to -1, 0, or 1.
So, the domain of $\cos^{-1}[x]$ is [-1, 2) (option D).