函数y等于2x减根号下x减1

题目

函数y等于2x减根号下x减1

答案

y=2x-√(x-1)
设z=√(x-1)≥0
y=2(x-1)-√(x-1)+2
=2z^2-z+2
=2[z-1/4]^2-1/8+2
=2[z-1/4]^2+15/8
z≥0
z-1/4≥-1/4
(z-1/4)^2≥0
(z-1/4)^2+15/8≥15/8
y≥15/8