5) у=2√х + √(3х-х²-2)
х-4
{x≥0
{x-4≠0
{3x-x²-2≥0
x-4≠0
x≠4
3x-x²-2≥0
x²-3x+2≤0
Парабола-ветви вверх.
х²-3х+2=0
Д=9-8=1
х₁=3-1=1
2
х₂=3+1=2
2
+ \\\\\\\\\\ +
------ 1 ---------- 2 ---------
-
х∈[1; 2]
{x≥0
{x≠4
{x∈[1; 2]
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
---- 0 ------ 1 -------- 2 ------- 4 --------
\\\\\\\\\\
х∈[1;2]
D(y)=[1; 2] - область определения функции
6) у=√х + √(1/(х-2))
{x≥0
{ 1 >0
x-2
1 >0
x-2
x-2>0
x>2
{x≥0
{x>2
\\\\\\\\\\\\\\\\\\\\\\\\\
-------- 0 ------- 2 ---------
\\\\\\\\\\\\\\\\\\\\
x∈(2; +∞)
D(y)=(2; +∞)