![y=7^{\cos^{2}x+1}-7 y=7^{\cos^{2}x+1}-7](https://tex.z-dn.net/?f=y%3D7%5E%7B%5Ccos%5E%7B2%7Dx%2B1%7D-7)
Решение:
1\medskip\\7^1\leq 7^{\cos^2 x+1}\leq 7^2,~|-7\medskip\\0\leq 7^{\cos^2 x+1}-7\leq 42\Leftrightarrow 0\leq y\leq 42 \Rightarrow E(y)=\left[0;42\right]" alt="-1\leq\cos x\leq 1,\medskip\\0\leq\cos^2 x\leq 1,~|+1\medskip\\1\leq\cos^2 x+1\leq 2,~|\, 7>1\medskip\\7^1\leq 7^{\cos^2 x+1}\leq 7^2,~|-7\medskip\\0\leq 7^{\cos^2 x+1}-7\leq 42\Leftrightarrow 0\leq y\leq 42 \Rightarrow E(y)=\left[0;42\right]" align="absmiddle" class="latex-formula">
Ответ. ![E(y)=\left[0;42\right] E(y)=\left[0;42\right]](https://tex.z-dn.net/?f=E%28y%29%3D%5Cleft%5B0%3B42%5Cright%5D)