Question

设x,y,z都是不超过1的非负实数,若k=x+y(1-x)+z(1-x)(1-y),求k的取值范围.

Answer 1

k=x+y(1-x)+z(1-x)(1-y)

=1-(1-x-y+xy)+z(1-x)(1-y)

=1-(1-x)(1-y)+z(1-x)(1-y)

=1-(1-x)(1-y)(1-z)

当x=y=z=0时

K最小值=0

当x=y=z=1时

K最大值=1