4-5(6x-6)<54-40x
4-30x+30<54-40x
-30x+40x<54-4-30
10x<20
x<20/10=2
x<2
<span>f(x)=x^2
</span>f(x-1)+f(x+1) = (x-1)^2 + (x+1)^2
= x^2 - 2x + 1 + x^2 + 2x + 1
= x^2 + 1 + x^2 + 1
= 2*(x^2) + 2
f(x+2)-f(x) = (x+2)^2 - x^2
= x^2 + 4x + 4 - x^2
= 4x + 4
Решение
а) y = 7 + √sin(x/2)
sinx/2 ≥ 0
arcsin0 + 2πn ≤ x/2 ≤ π - arcsin0 + 2πn, n ∈ Z
2πn ≤ x/2 ≤ π + 2πn, n ∈ Z
4πn ≤ x ≤ 2π + 4πn, n ∈ Z
б) y = 10 - √cos(x/3)
cosx/3 ≥ 0
- arccos0 + 2πk ≤ x/3 ≤ arccos0 + 2πk, k ∈ Z
- π/2 + 2πk ≤ x/3 ≤ π/2 + 2πk, k ∈ Z
- 3π/2 + 6πk ≤ x ≤ 3π/2 + 6πk, k ∈ Z
А) ОДЗ: хє(-бесконечности;-√3]U[√3;бесконечности)
х2-х-6<0
-2<х<3
Ответ: хє(-2;-√3]U[√3;3)