Question

For the function $f\left(x\right)=sin\left(\pi \left[x\right]\right)\times cos^{- 1}\left(\left[x\right]\right)$ , choose the correct option.

(where $\left[.\right]$ represents the greatest integer function)

• A. Domain of $f\left(x\right)\in \left[- 1,1\right]$
• B. Range of $f\left(x\right)$ contains exactly two elements
• C. $f\left(x\right)$ is an identity function
• D. $f\left(x\right)$ is a constant function

Answer 1

Answer: (D)

For any $x \in R,$ we know,
$\sin \pi[x]=0$
$\therefore f(x)=0, \forall x \in[-1,2)\left\{\because-1 \leq[x] \leq 1\right.$ for $\cos ^{-1}[x]$ to be defin ed $\}$
$\therefore $ Domain $x \in[-1,2)$
$\Rightarrow $ Range $=\{0\}$
$\therefore f(x)$ is a constant function