Question

Salut.
Se considera functia f:R>R, f(x)=2x-5. Determinati numarul real a pentru care f(a)-f(2)=2f(4)

Answer 1

Răspuns:

f(2)= 2×2-5 = 4-5 = -1

f(4)= 2×4-5 = 8-5 = 3

f(a)-(-1)= 2×3 ===> f(a) +1 = 6 ===> f(a)= 6-1 =5

f(a)=5 ===> 2a-5 = 5 ===> 2a = 5+5 ===> 2a =10 ===> a=5

Answer 2

$\it f(x)=2x-5\ \ \ \ \ (*)\\ \\ f(a)-f(2)=2f(4)\ \stackrel{(*)}{\Longrightarrow}\ 2a-5-(2\cdot2-5)=2(2\cdot4-5) \Rightarrow \\ \\ \Rightarrow 2a-5+1=6 \Rightarrow 2a-4=6|_{+4} \Rightarrow 2a=10|_{:2} \Rightarrow a=5$