FunctionHard
Question
If F(x) = 
, then F (x) is: (where { . } denotes fractional part function and [. . ] denotes greatest integer function and sgn (x) is a signum function)
, then F (x) is: (where { . } denotes fractional part function and [. . ] denotes greatest integer function and sgn (x) is a signum function)Options
A.periodic with fundamental period 1
B.even
C.range is singleton
D.identical to sgn 
- 1
- 1Solution
f(x) =
= 0 , x ∈ I (A) By graph fundamental period is one
(B) f(-x) = 0 = f(x) ∴ even function
(C) Range y ∈{0}
(D) y = sgn
- 1, x ∈ I y = sgn (1) - 1 ⇒ y = 1 - 1
y = 0, x ∈ I Identical to f(x)
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