Question

函数fx=x+根号(2-x) 的值域是什么

Answer 1

f(x)=x+√(2-x)

2-x≥0,定义域x≤2

f'(x)=1-1/{2√(2-x)} = {2√(2-x) - 1} / {2√(2-x)}

x＜7/4时,f'(x)＞0,f(x)单调增；7/4＜x＜2时,f'(x)＜0,f(x)单调减

x=7/4时,最大值ymax=7/4+√(2-7/4)=9/4

值域（-无穷大,9/4]