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Q.
If $f (\theta)=\min .(|2 x -7|+| x -4|+| x -2-\sin \theta|)$, where $x , \theta \in R$, then maximum value of $f (\theta)$ is
Relations and Functions - Part 2
Solution:
$f (\theta)=\min .(|2 x -7|+| x -4|+| x -2-\sin \theta|)$
Let $g(x)=|2 x-7|+|x-4|+|x-2-\sin \theta|$
$\left.g(x)\right|_{\min }=g\left(\frac{7}{2}\right)=\frac{1}{2}+\frac{3}{2}-\sin \theta=2-\sin \theta=f(\theta)$
$\left.\therefore f (\theta)\right|_{\max }=3$