Question

Find the domain for function f(x)=[sin⁡x]cos⁡(π[x−1])

• A. (A) [1, 2]
• B. (B) (−∞,1)∪[2,∞)
• C. (C) x∈R
• D. (D) None of these

Answer 1

Answer: (B)

(B) (−∞,1)∪[2,∞)

Answer 2

Explanation:
Given:f(x)=[sin⁡x]cos⁡(π[x−1])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 ∀×∈Rcos⁡(π∣x−1]) is always defined every where except when[x−1]=0[ Because π0 do not exist ]⇒0≤x−1<1⇒1≤x<2∴ Domain of f(x)=R−[1,2]=(−∞,1) ∪ [2,∞]Hence, the correct option is (B).