Question

Let $f\left(x\right)=\left\{x\right\}.$ Then which of the following(s) is/are correct
(where $\{.\}$ represents the fractional part function)

• A. $f\left(1^{-}\right)=1$
• B. $f\left(1\right)=0$
• C. $x=1$ is the point of minimum.
• D. $x=1$ is the point of maximum

Answer 1

Answer: (A), (B), (C)

$x=1$ is the point of minimum.

Given : $f\left(x\right)=\left\{x\right\}$


From the diagram of $f\left(x\right)=\left\{x\right\}$
$f\left(1\right)=0,f(1-h)=1-h$ and $f(1+h)=h$ as $h\to 0^{+}$
$\Rightarrow f(1+h)>0$ and $f(1-h)>0$
$\therefore$ $x=1$ is the point of minimum.