Question

determine whether the follwoing fuction is odd or even
f(x)=[x]+1/2

Answer 1

Step-by-step explanation:

Correct option is

A

f is an even function when x∈Z, f is an odd function when x∈

/

Z

C

f is an even function for all integers

D

Neither odd nor even

Let f:R→R be a function defined as f(x)=(−1)

[x]

.

When x is an integer [x]=x, hence f(x)=(−1)

[x]

=(−1)

x

, which is an even function.

If x is a positive real number which is not an integer, then [x] is the integer part of the given number, say a.

Therefore f(x)=±1 based on a is even or odd.

If x is a negative real number which is not an integer, then [x]=a−1, where a is the integer part of the given number.

Therefore f(x)=±1 based on a is odd or even.

Hence f(x)=−f(−x) when x∈

/

Z