Question

varianta 2
vă rog am nevoie urgent​

Answer 1

Răspuns:

Explicație pas cu pas:

1) numere intregi din intervalul : (-√11 ; 2,7] sunt:

{-3 ; -2 ; -1 ; 0 ; 1 ; 2}

2) A = [-2 ; 5) ; B = (-3 ; 4]

A ∪ B =  [-2 ; 5) ∪ (-3 ; 4] = (-3 ; 5)

A ∩ B = [-2 ; 5) ∩ (-3 ; 4] = [-2 ; 4]

A-B = (4 ; 5)

B-A = (-3 ; -2)

3) f,g : R --> R ; f(x) = (5-x)/2  ; g(x) = 5x+1

a) f(x) = g(x) <=>  (5-x)/2 = 5x+1 => 5-x = 10x+2 =>

10x+x = 5-2 => 11x = 3 => x = 3/11

b) f(x) ≥ g(x) <=> (5-x)/2 ≥ ²⁾5x+1 => 5-x ≥ 10x+2 =>

5-2 ≥ 10x+x <=> 3 ≥ 11x => 11x ≤ 3 => x ≤ 3/11 => x ∈ (-∞ ; 3/11]

4) 2(x+1) < 4-3(x-2) <=> 2x+2 < 4-3x+6 <=> 2x+3x < 4+6-2 =>

5x < 8 => x < 8/5 => x ∈ (-∞ ; 8/5)

Cea mai mare solutie intreaga = 1 ; Cea mai mica --> -∞

5) x/√(4-3x)  ; √(4-3x) ≠ 0 =>  4-3x > 0 => 4 > 3x =>

3x < 4 => x < 4/3 => x ∈ (-∞ ; 4/3)

6) a - b = 73 ; a: b = 5 rest 9 <=> a = 5b + 9 =>

5b+9 -b = 73 => 4b = 73-9 => 4b = 64 => b = 64:4 => b = 16 ;

a = 5·16+9 => a = 89

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