Question

a) Determinaţi funcția f: R+R, de forma
f(x) = ax + b al cărei grafic trece prin
punctele A(2; 1), B(6; -1)!!!!​

Answer 1

Răspuns:

$f(x)=ax+b$

$A(2,1);B(6,-1)=>\\f(2)=1 <=>2a+b=1\\f(6)=-1<=>6a+b=-1|*(-1)\\2a+b=1 (1)\\-6a-b=1(2)\\(1)+(2)=2a-6a+b-b=1+1<=>-4a=2=>a=-\frac{1}{2}\\=> b=1-2a=1-2(-\frac{1}{2})=>b=2$

$f(x)=-\frac{1}{2}x+2$