Question

Let $f\left(x\right)=(1{)}^{\left[x\right]}$ (where [.] denotes the greatest integer function), then which of the following is not true?

• A. Range of $f$ is $\left\{1\right\}$
• B. $f$ is an even function
• C. $f$ is an odd function
• D. $\underset{x\to n}{lim}f\left(x\right)$ exists, for every integer $n$

Answer 1

The correct option is C $f$ is an odd function

$f\left(x\right)=(1{)}^{\left[x\right]}=1$ since, $\left[x\right]$ is integer
Therefore, $f\left(x\right)\in 1$
and $f\left(x\right)=1$ is an even function
And ${lim}_{x\to n}f\left(x\right)=1$ for every integer $n$