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### range of f(x)

Posted: Thu Feb 07, 2013 11:58 am
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 $f(x_{0}) = \alpha$