Question

2. Fie functia f : IR -> IR , f(x) = 5x-2.
a) Reprezentati grafic functia intr-un sistem de axe xOy.
b) Rezolvati in IR ecuatia , f(a) + f(a+1) = f(a - 2 ).
c) Calculati suma S= f(1) + f(2) + f(3) + ... + f( 50)

Answer 1

a) Aflam intersectia graficului funtiei cu axele de coordonate si stabilim cele doua puncte, prin care reprezentam grafic functia :
$f(x)=5x-2 \\ f(0)=-2; A(0;-2) \\ f(x)=5x-2=0;x= \frac{2}{5} ;B(\frac{2}{5} ;0)$
b) $f(a)+f(a+1)=f(a-2) \\ 5a-2+5(a+1)-2=5(a-2)-2 \\ 5a-2+5a+5-2=5a-10-2 \\ 5a=-12-1 \\ 5a=-13 \\ a= -\frac{13}{5}$
c) $f(1)+f(2)+f(3)+...+f(50)= \\ =5*1-2+5*2-2+5*3-2+...+5*50-2= \\ =5*(1+2+3+...+50)-2*50= \\ =5* \frac{50*51}{2} -100=6375-100=6275$