The function f : R→R is defined f(x)=cos2 x+sin4 x for x∈R. Then the range of f(x) is

y=f(x)=cos2⁡x+sin4⁡x=cos2⁡x+sin2⁡x1−cos2⁡x=cos2⁡x+sin2⁡x−sin2⁡xcos2⁡x=1−sin2⁡xcos2⁡x=1−14sin2⁡2x∴    34≤f(x)≤1 ∵0≤sin2⁡2x≤1∴     f(x)∈[3/4,1]