FunctionEasy
Question
If f(x) = sgn 
, where [.] is the greatest integer function, then which of the following statement is/are true ?
, where [.] is the greatest integer function, then which of the following statement is/are true ?Options
A.
f(x) = 1
f(x) = 1B.Range of f(x) contains only one integer
C.f(x) is periodic function.
D.The equation f(x) = 1 + 
x2 dt has infinitely many non-integral roots.
x2 dt has infinitely many non-integral roots.Solution
f(x) = sgn
.domain of the function is x ∈ [2n, 2n+1) where
n ∈ I. and tan
= 0 ⇒ ∀ x ∈ [2n,2n + 1)and sgn
= 1 for x in domain∴ f(x) = 1 ∀ x ∈ [2n, 2n + 1) graph of y = f(x)
Also, f(x) = 1 +
x2dt = 1 + x2 - 1⇒ x2 = 0
⇒ x = 0 only one root.
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