作业帮（根号x +1）/(x+3) x属于[0,1/4]急
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 08:08:29
![（根号x +1）/(x+3) x属于[0,1/4]急](/uploads/image/z/2087164-28-4.jpg?t=%EF%BC%88%E6%A0%B9%E5%8F%B7x+%2B1%EF%BC%89%2F%28x%2B3%29+x%E5%B1%9E%E4%BA%8E%5B0%2C1%2F4%5D%E6%80%A5)
（根号x +1）/(x+3) x属于[0,1/4]急
（根号x +1）/(x+3) x属于[0,1/4]
急
（根号x +1）/(x+3) x属于[0,1/4]急
设根号X+1=T,则X=(T-1)^2=T^2-2T+1
X+3=T^2-2T+4,则(根号X+1)/(X+3)=T/(T^2-2T+4)=1/(T+4/T-2)
因为X属于[0,1/4],则T属于[1,3/2]
T+4/T属于[25/6,5],则所求值域为[1/3,6/13]