Question

Let f(x) = [x]+[–x]. Then for any integer m and non integer a, which of the following statements is/are wrong

• A. $\underset{x\to m}{lim}f\left(x\right)exist$
  
• B. f(x) is continuous at x = m
  
• C. f(x) is continuous at x = a
  
• D. $\underset{x\to a}{lim}f\left(x\right)exists$

Answer 1

The correct option is B f(x) is continuous at x = m




$f\left(x\right)=\left[x\right]+[-x]=\{\begin{array}{cc}0:& xϵZ\\ -1:& x\text{/}ϵZ.\end{array}$
$\therefore \underset{x\to m}{lim}f\left(x\right)=-1\ne f\left(m\right)$ and $\underset{x\to a}{lim}f\left(x\right)=-1=f\left(a\right)$
$\Rightarrow$ (i), (iii) and (iv) are correct.