Question

Find the domain for function $$f(x)=[\sin x]\cos \left(\frac{\pi }{[x-1]}\right)$$

• (A) [1, 2]
• (B) $(-\mathrm{\infty },1)\cup [2,\mathrm{\infty })$
• (C) $x\in R$
• (D) None of these

Answer 1

The Correct Option is B

Explanation:
Given:$f(x)=[\sin x]\cos \left(\frac{\pi }{[x-1]}\right)$We have to find the domain of $f(x)$.Using definition of sine function, cosine function and greatest integer function, we have$[\sin x]$ is always defined $\mathrm{\forall }\times \in R$$\cos \left(\frac{\pi }{\mid x-1]}\right)$ is always defined every where except when$[\mathrm{x}-1]=0\left[\text{Because}\frac{\pi }{0}\text{do not exist}\right]$$\Rightarrow 0\le x-1<1$$\Rightarrow 1\le x<2$$\therefore$ Domain of $f(x)=R-[1,2]=(-\mathrm{\infty },1)\cup [2,\mathrm{\infty }]$Hence, the correct option is (B).