Question

Ajutati-ma ! Va rog!

Answer 1

a)f(-2) = 7

f(1) = -2

-2a + b = 7

a + b = -2

a = -2 -b = -(b + 2)

2(b + 2) + b = 7

2b + 4 + b = 7

3b = 3

b = 1

a = -(1 + 2) = -3

f(x) = -3x + 1

b)

$f(a+b)\leq f(a) + f(b)\\a(a+b) \leq a^2 + b + ab + b\\a^2 + ab \leq a^2 + 2b + ab\\0 \leq 2b\\2b \geq 0\\b \geq 0\\b\in [0,+\infty)$

c)

$g(-1)=-3\cdot(-1) + 1 = 6 + 1 = 7\\g(2) = -3\cdot 2 + 1 = -6+1 = -5\\Im\:g = [-5,7]$

Valorile functiei $g$ sunt din intervalul [-5,7]