48.2. Find the range of the function

$$
f(x)=\sin ^{6} x+\cos ^{6} x
$$
48.2. We have: $f(x)=\sin ^{6} x+\cos ^{6} x=\left(\sin ^{2} x+\cos ^{2} x\right)^{3}-3 \sin ^{4} x$. - $\cos ^{2} x-3 \sin ^{2} x \cdot \cos ^{4} x=1-0.75 \sin ^{2} 2 x$. Since $0 \leqslant \sin ^{2} 2 x \leqslant 1$, then $0.25 \leqslant 1-0.75 \sin ^{2} 2 x \leqslant 1$.