Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If F (x) = 
, then F (x) is: (where { . } denotes fractional part function and [ . . ] denotes greatest integer function and sgn (x) is a signum function)
A
periodic with fundamental period 1
B
even
C
range is singleton
D
identical to sgn 
− 1
− 1
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,b,c,d)
f(x) = 
= 0 , x ∉ Ι
By graph fundamental period is one
f(–x) = 0 = f(x) ∴ even function
Range y ∈ {0}
y = sgn – 1, x ∉ Ι
y = sgn 
(1) – 1 ⇒ y = 1 – 1
y = 0, x ∉ Ι Identical to f(x)
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