Question

Fie f : R -> R , f(x) = 3/2 x -27. Calculati produsul P = f(10)·f(11)·f(12)·...·f(20).

Answer 1

$f:R\Rightarrow R,f(x)=\frac{3x}{2}-27=\frac{3x-54}{2}$
$f(10)f(11)...f(20)=\frac{3*10-54}{2}*\frac{3*11-54}{2}*...*\frac{3*20-54}{2}=$
$=\frac{-24*(-21)*...*(3*18-54)*...*(6)}{2^{11}}=0$
3*18=54
Deci produsul este 0.
Sau solutia mai usoara
$f(x)=\frac{3x}{2}-27=\frac{3x-54}{2}$
$f(18)=0$
Deci f(10)f(11)...f(20)=0