Question

The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:

• A. $[2 \sqrt{2}, \sqrt{11}]$
• B. $[\sqrt{5}, \sqrt{10}]$
• C. $[\sqrt{5}, \sqrt{13}]$
• D. $[\sqrt{2}, \sqrt{7}]$

Answer 1

Answer: (B)

$ y^2=3-x+2+x+2 \sqrt{(3-x)(2+x)}$
$ =5+2 \sqrt{6+x-x^2} $
$ y^2=5+2 \sqrt{\frac{25}{4}-\left(x-\frac{1}{2}\right)^2}$
$ y_{\max }=\sqrt{5+5}=\sqrt{10} $
$ y_{\min }=\sqrt{5}$