If the range of the function f(x) = 
+ cos π 
+ sin 
is 
∪ 
∪ 
, (where {.} and [.] represent fractional part and greatest integer part functions respectively), then α 2 + β 2 + γ 2 + δ 2 is
Text Solution
Verified by Experts15
(15)
Sol. Period of 
is 4 ⇒ cos π 
= 0 ∀ x ∈ R
Period of sin 
is 4
∴ Period of f(x) is 4. For periodic function f(x) range can be calculated for x ∈ [0, 4]
If x ∈ [0, 1) ; f(x) = 
, f(x) ∈ 
; If x ∈ [1, 2) ; f(x) = 
+ 1 , f(x) ∈ 
If x ∈ [2, 3) ; f(x) = 
, f(x) ∈ 
; If x ∈ [3, 4) ; f(x) = 
– 1, f(x) ∈ 
Range ∈ 
∪ 
∪ 
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