1) y=√(log₀.₅(4x-1))
{log₀.₅(4x-1)≥0
{4x-1>0
log₀.₅(4x-1)≥log₀.₅ 1
{4x-1 ≤1
{4x-1>0
{4x≤1+1
{4x>1
{4x≤2
{x>0.25
{x≤1/2
{x>1/4
x∈(1/4; 1/2)
D(y)=(1/4; 1/2) - область определения функции.
Ответ: (1/4; 1/2)
2) y=ln²(x²-3x)
√(5x+1)
{x²-3x>0
{5x+1>0
x²-3x>0
x(x-3)>0
x=0 x=3
+ - +
--------- 0 ----------- 3 -------------
\\\\\\\\\ \\\\\\\\\\\\\\\
x∈(-∞; 0)U(3; +∞)
5x+1>0
5x>-1
x>-0.2
x∈(-0.2; 0)U(3; +∞)
D(y)=(-0.2; 0)U(3; +∞) - область определения.