Question

求函数y=(1+x^1/2)/(2-x^1/2)的值域

Answer 1

y*(2-根号X)=1+根号X

2Y-Y根号X=1+根号X
2Y-1=(Y+1)根号X
根号X=(2Y-1)/(Y+1)>=0
即得到Y>=1/2或Y<-1
即值域是(-无穷,-1)U[1/2,+无穷)

Answer 2

设x^1/2=t 有t≥0 而y=(1+t)(2-t)=-t²+t+2 得y≤4/9