Question

已知函数fx=（sinx+cosx）^2+2cos^2x-2 当x属于[派/4,3派/4]时,求

Answer 1

你好,

f(x)=sin^2x+cos^2x+2sinxcosx+cos2x-1

=1+sin2x+cos2x-1

=sin2x+cos2x

=根号下2(sin(2x+π/4))

x∈【π/4,3π/4】

2x+π/4∈【3π/4,7π/4】

当x=3π/2时,f(x)=-根号下2

当x=π/4时,f(x)=1

所以f(x)∈【-根号下2,1】