Question

Fie functia liniara f:R->R,care indeplineste conditia f(x-1)= -2x+6.
a) Determinati functia;
b) Determinati punctele de pe grafic care au ordonata egala cu dublul abscisei

Answer 1

$f(x-1)=-2x+6 \\ f(x-1)=a(x-1)+b \\ ax-a+b=-2x+6 \\ \left \{ {{a=-2} \atop {-a+b=6}} \right. \Leftrightarrow \left \{ {{a=-2} \atop {b=4}} \right. \\ f(x)=-2x+4 \\ \\ \\ f(x)=2x \\ -2x+4=2x \\ -4x+4=0 \\ x=1 \Rightarrow A(1,2)$

Answer 2

a. f(x-1)=-2x+2+4=-2(x-1)+4, deci f(x)=-2x+4

b. A(x, 2x), 2x=-2x+4, 4x=4, x=1   A(1, 2)