Question

Sa se determine functia f:R->R, f(x) = ax+b stiind ca: f(-1) = 2 si f(3) = -4.

Answer 1

$f(x)=ax+b\\f(-1)=2\Rightarrow -a+b=2\Rightarrow b=2+a\\f(3)=-4\Rightarrow 3a+b=-4\\3a+2+a=-4\\4a=-6\Rightarrow\displaystyle a=-\frac32\\\displaystyle b=2-\frac32=\frac12\\\\\displaystyle f(x)=-\frac32x+\frac12=\frac{-3x+1}{2}$