The function f : R → R is defined by for $f(x)=\cos^2x+\sin^4x$ for x ∈ R, then what is the range of f.

$[\frac{1}{4},1]$ $[\frac{1}{2},1]$ $[\frac{3}{4},1]$ $[\frac{1}{9},1]$

$[\frac{3}{4},1]$

$f(x)=\cos^2x+\sin^4x$ $y=f(x)=\cos^2x+\sin^2x(1-\cos^2x)$ $y=\cos^2x+\sin^2x-\sin^2x\cos^2x$ $y=1-\sin^2x\cos^2x$ $y=1-[\frac{1}{4}]×[\sin^22x]$ $\frac{3}{4}≤f(x)≤1$, (Because $0≤\sin^22x≤1$) $f(R)∈[\frac{3}{4},1]$