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