## range of f(x)

For students of class 11-12 (age 16+)
jagdish
Posts: 38
Joined: Wed Jan 19, 2011 2:21 pm
Let the range of the function $f:\mathbb{R}\rightarrow \mathbb{R}$ and $f(x) = | x-1| + |x - a| + | x| + |x+1| + |x+ 2a - 21 |$
given by $\left[\alpha,\infty \right)$
where $a$ being a real parameter .
Then find the number of integral values of $a$ for which there is exactly one $x_{0}\in\mathbb{R}$
such that $f(x_{0}) = \alpha$