Question

Помогите пж с первым заданием

Answer 1

$1) \ y = \text{lg}(5x - 3)$

$D(y) = 5x - 3 > 0; \ 5x > 3; \ x > \dfrac{3}{5}$

$\text{OTBET:} \ x \in \bigg( \dfrac{3}{5}; +\infty \bigg)$

$2) \ y = \text{lg}(1 + \text{sin} \ x)$

$D(y): 1 + \text{sin} \ x > 0\\t_{1} + 2\pi n < x < t_{2} + 2\pi n$

$t_{1} = \text{arcsin}(-1) = -\dfrac{\pi}{2} \\t_{2} = \pi - \bigg(-\dfrac{\pi}{2} \bigg) = \dfrac{3\pi}{2}$

$-\dfrac{\pi}{2} + 2\pi n < x < \dfrac{3 \pi }{2} + 2 \pi n, \ n \in Z$

$\text{OTBET:} \ x \in \bigg( -\dfrac{\pi}{2} + 2\pi n; \ \dfrac{3 \pi }{2} + 2 \pi n \bigg), n \in Z$