Question

Mulțumesc anticipat!

Answer 1

Răspuns:

Explicație pas cu pas:

f(x)=-5x+1, deci f(m-1)=-5·(m-1)+1=-5m+5+1=-5m+6

f(m)=-5m+1;  f(m+1)=-5(m+1)+1=-5m-5+1=-5m-4.

Atunci din f(m-1)+f(m)+f(m+1)=0, ⇒-5m+6-5m+1-5m-4=0, ⇒-15m+3=0, ⇒-15m=-3, ⇒m=-3:(-15)=1/5.

b) f(2)=-5·2+1=-10+1=-9;  f(3)=-5·3+1=-15+1=-14. Atunci obtinem inecuatia

2·(-5x+1)-(-9)≤-14, ⇒-10x+2+9≤-14, ⇒-10x≤-14-11, ⇒-10x≤-25, ⇒x≥(-25):(-10), deci x≥2,5.

Answer 2

Răspuns:

Explicație pas cu pas:

f(x) = -5x + 1

f(m-1) + f(m) + f(m+1) = 0

-5(m - 1) + 1 - 5m + 1 -5(m + 1) + 1 = 0

-5m + 5 + 1 - 5m + 1 - 5m - 5 + 1 = 0

-15m + 3 = 0

15m = 3

m = 3/15 = 1/5

_______________

f(x) = -5x + 1

2f(x) - f(2) ≤ f(3)

2(-5x + 1) - (-10 + 1) ≤ -15 + 1

-10x + 2 + 10 - 1 ≤ -14

-10x + 11 ≤ -14

-10x ≤ -25

10x ≥ 25

x ≥ 25/10

x ≥ 5/2