Question

If $\alpha$ is a real number for which f(x) = ${\cos }^{-1}x$ is defined then a possible value of $\left[\alpha \right]$ is (where [ .] denotes greatest integer function)

• A. 2
• B. 1
• C. -1
• D. -2

Answer 1

Answer: (B), (C)

1
-1

Greater integer function :-

For all real numbers of $x$ the G.I.F returns the largest integer less than or equal to $x$. It rounds down a real number to the nearest integer.

Ex :- $\left[1\right]=1:\left[1.5\right]=1:\left[4.3\right]=4$

$f\left(x\right)={cos}^{-1}x$

Domain of ${cos}^{-1}x$ is $[-1,1]$

So, $[-1]=-1:\left[1\right]=1$

The possible values of $\left[\alpha \right]$ is $1$ and $-1$.