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Q.
The domain of the function $\sqrt{x^{2}-5x+6} + \sqrt{2x+8-x^{2}}$ is
Relations and Functions
Solution:
$f\left(x\right) = \sqrt{\left(x-2\right)\left(x-3\right)} + \sqrt{-\left(x-4\right)\left(x+2\right)}$
The first part is real outside $\left(2,\, 3\right)$ and the second is real in $\left[-2,\, 4\right]$ so that the domain is $\left[-2,\, 2\right] \cup \left[3, \,4\right].$