Solve y=sqrt{2x-1}+sqrt{4-x}

$$y = \sqrt { 2 x - 1 } + \sqrt { 4 - x }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{2}=0.5\text{; }x=4\text{, }&|-arg(-y)+\pi |<\pi \\x=\frac{2\sqrt{y^{2}\left(21-2y^{2}\right)}+y^{2}+15}{9}\text{, }&|-arg(-y)+arg(-\sqrt{2x-1}-\sqrt{4-x})|<\pi \text{ and }|arg(\sqrt{-2\sqrt{21y^{2}-2y^{4}}-y^{2}+21}\sqrt{4\sqrt{21y^{2}-2y^{4}}+2y^{2}+21})-arg(-\frac{\sqrt{21y^{2}-2y^{4}}}{9}+\frac{4y^{2}}{9}-\frac{7}{3})|<\pi \text{ and }y\neq -\sqrt{7}\text{ and }y\neq \sqrt{7}\\x=\frac{-2\sqrt{y^{2}\left(21-2y^{2}\right)}+y^{2}+15}{9}\text{, }&|-arg(-y)+arg(-\sqrt{2x-1}-\sqrt{4-x})|<\pi \text{ and }|arg(\sqrt{-4\sqrt{21y^{2}-2y^{4}}+2y^{2}+21}\sqrt{2\sqrt{21y^{2}-2y^{4}}-y^{2}+21})-arg(\frac{\sqrt{21y^{2}-2y^{4}}}{9}+\frac{4y^{2}}{9}-\frac{7}{3})|<\pi \text{ and }y\neq -\frac{\sqrt{14}}{2}\text{ and }y\neq \frac{\sqrt{14}}{2}\end{matrix}\right.$$

Solve for y

$$y=\sqrt{2x-1}+\sqrt{4-x}$$

$$x\geq \frac{1}{2}\text{ and }x\leq 4$$