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1. Парабола должна быть неотрицательной, следовательно,
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Answers & Comments
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г)![\sqrt[3]{log_2(2tg(\frac{\pi}{4}))} = \sqrt[3]{log_2(2)} = 1](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Blog_2%282tg%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%29%7D%20%3D%20%5Csqrt%5B3%5D%7Blog_2%282%29%7D%20%3D%201 "\sqrt[3]{log_2(2tg(\frac{\pi}{4}))} = \sqrt[3]{log_2(2)} = 1")
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a)![\sqrt[5]{10^x}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7B10%5Ex%7D "\sqrt[5]{10^x}")
б)![10^{\sqrt[5]{x}}](https://tex.z-dn.net/?f=10%5E%7B%5Csqrt%5B5%5D%7Bx%7D%7D "10^{\sqrt[5]{x}}")
в)![\sqrt[5]{tg(10^x)}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Btg%2810%5Ex%29%7D "\sqrt[5]{tg(10^x)}")
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1. Парабола должна быть неотрицательной, следовательно,![D(f) = (-\infty; -2]\cup[\frac{4}{3}; \infty)](https://tex.z-dn.net/?f=D%28f%29%20%3D%20%28-%5Cinfty%3B%20-2%5D%5Ccup%5B%5Cfrac%7B4%7D%7B3%7D%3B%20%5Cinfty%29 "D(f) = (-\infty; -2]\cup[\frac{4}{3}; \infty)")
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3.![D(f) = (-4; -3) \cup (-3; 7]](https://tex.z-dn.net/?f=D%28f%29%20%3D%20%28-4%3B%20-3%29%20%5Ccup%20%28-3%3B%207%5D "D(f) = (-4; -3) \cup (-3; 7]")
4.![D(f) = [1; \frac{\pi}{2}]](https://tex.z-dn.net/?f=D%28f%29%20%3D%20%5B1%3B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%5D "D(f) = [1; \frac{\pi}{2}]")
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2.![E(f) = [2; 3]](https://tex.z-dn.net/?f=E%28f%29%20%3D%20%5B2%3B%203%5D "E(f) = [2; 3]")
3.![3sin(x) + 4cos(x) = 5(\frac{3}{5}sin(x) + \frac{4}{5}cos(x)) = 5sin(x + arcsin(\frac{3}{5})) \rightarrow E(f) = [-5;5]](https://tex.z-dn.net/?f=3sin%28x%29%20%2B%204cos%28x%29%20%3D%205%28%5Cfrac%7B3%7D%7B5%7Dsin%28x%29%20%2B%20%5Cfrac%7B4%7D%7B5%7Dcos%28x%29%29%20%3D%205sin%28x%20%2B%20arcsin%28%5Cfrac%7B3%7D%7B5%7D%29%29%20%5Crightarrow%20E%28f%29%20%3D%20%5B-5%3B5%5D "3sin(x) + 4cos(x) = 5(\frac{3}{5}sin(x) + \frac{4}{5}cos(x)) = 5sin(x + arcsin(\frac{3}{5})) \rightarrow E(f) = [-5;5]")
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