If f : R → R is defined as f ( x ) = x - [ x ] + 3 , ∀ x ∈ R , then f is

If f:R→R is defined as f(x)=x-[x]+3,∀x∈R, then f is
  1. not a function
  2. a periodic function with period π
  3. a periodic function with period 1
  4. an invertible function

Solution

f:R→R

f(x)=x-[x]+3

⇒f(x)={x}+3

{x} is periodic with period

So, f(x) is periodic with period 1.

Asked in: AP EAMCET 2020 (23 Sep Shift 1)

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