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)
Create a free account to view solution
View Solution FreeMore Function Questions
Given f(x) = log and g(x) = , then (fog) (x) equals -...If f : R → R, f(x) = x2, then {x| f (x) = −1} equals-...Function f(x) = is monotonic decreasing in-...If f : I → I, f(x) = x2 − x, then f is -...Let f(x) = If f (x) is an even function in R then the definition of f(x) in (0, ∞) is -...