The function $f:R\to R$ is defined by $f\left(x\right)={\cos }^{2}x+{\sin }^{4}x$ or $x\in R$ Then the range of $f\left(x\right)$ is

$\begin{array}{l}y=f\left(x\right)={\cos }^{2}x+{\sin }^{4}x\\ ={\cos }^{2}x+{\sin }^{2}x\left(1-{\cos }^{2}x\right)\\ ={\cos }^{2}x+{\sin }^{2}x-{\sin }^{2}x{\cos }^{2}x\\ =1-{\sin }^{2}x{\cos }^{2}x\\ =1-\frac{1}{4}{\sin }^{2}2x\\ \therefore \frac{3}{4}\le f\left(x\right)\le 1 \left( 0\le {\sin }^{2}2x\le 1\right)\\ \therefore f\left(x\right)\in \left[3/4,1\right]\end{array}$