Question

If $f(x)=|x-1|+|x-2|+|x-3|, 2< x < 3$ then $f$ is

• A. an onto function but not one-one
• B. one-one function but not onto
• C. a bijection
• D. neither one-one nor onto

Answer 1

Answer: (C)

Given,
$f(x)=|x-1|+|x-2|+|x-3|$
$\Rightarrow f(x)=\begin{cases}6-3 x, & x< 1 \\ 4-x, & 1< x < 2 \\ x, & 2< x< 3 \\ 3 x-6, & x>3\end{cases}.$
When, $2 < x < 3 $, then $f(x)=x$
So, $f(x)=x$ is one-one and onto function.
$\therefore f(x)$ is a bijective.