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)

Options

A.periodic with fundamental period 1
B.even
C.range is singleton
D.identical to sgn - 1

Solution

     
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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