Răspuns:
2x - y ∈ [-5 ; 10]
{-3 ; 1 ; 3 ; 7}
Explicație pas cu pas:
3) x ∈ [-1 ; 4] ; y ∈ [-2 ; 3] => 2x - y ∈ ??
x = -1 ; y = 3 => 2x - y = 2·(-1) - 3 = -2 - 3 = -5
x = 4 ; y = -2 => 2x - y = 2·4 - (-2) = 8 + 2 = 10
=> 2x - y ∈ [-5 ; 10]
5) x ∈ Z I (2x+1)/(x-2) ∈ Z
x = -3 => [2· (-3)+1)/(-3-2)] = (-6+1)/(-5) = -5/(-5 )= 1 ∈Z
x = 1 => (2·1+1)/(1-2) = 3/(-1) = -3 ∈ Z
x = 3 => (2·3+1)/(3-2) = 7/1 = 7 ∈ Z
x = 7 => (2·7+1)/(7-2) = 15/5 = 3 ∈ Z
{-3 ; 1 ; 3 ; 7}
