Question

The domain of the function $\sqrt{x^2-5x+6}+\sqrt{2x+8-x^2}$ is

• A. $[2,3]$
• B. $[-2,4]$
• C. $[-2,2]\cup [3,4]$
• D. $[-2,1]\cup [2,4]$

Answer 1

Answer: (C)

$f\left(x\right)=\sqrt{\left(x-2\right)\left(x-3\right)}+\sqrt{-\left(x-4\right)\left(x+2\right)}$
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 $\left[-2,2\right]\cup \left[3,4\right].$