Question

Помогите пж с первым заданием

Answer 1

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

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

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

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

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

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

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

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