UPSEE Solved Model Paper 7

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 for all x ∊ R,
cos (

π

[x−1]

) is also defined every where except when
[x - 1] = 0 [Because π/0 does not exist]
⇒ 0 ≤ x - 1 < 1
⇒ 1 ≤ x < 2
∴ Domain of f (x) = R - [1 , 2) = (- ∞ , 1) ∪ [2, ∞)
Hence, option 'B' is correct.