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.
Answer & explanation
Correct answer: option 3
$f(x)=\cos^2x+\sin^4x$
$y=f(x)=\cos^2x+\sin^2x(1-\cos^2x)$
$y=\cos^2x+\sin^2x-\sin^2x\cos^2x$
$y=1-\sin^2x\cos^2x$
$y=1-[\frac{1}{4}]×[\sin^22x]$
$\frac{3}{4}≤f(x)≤1$, (Because $0≤\sin^22x≤1$)
$f(R)∈[\frac{3}{4},1]$