Question

Fie functia f:R-R,data de relatia f(2-3x)=6x-8.
a)Determinati f(x).

Answer 1

$\ Consideram f(x) = ax+b \\ \\ f(2-3x) = 6x-8 \Rightarrow a(2-3x) + b = 6x-8 \Rightarrow \\ \Rightarrow 2a-3ax +b = 6x-8\Rghtarrow \Rightarrow-3ax +2a+b = 6x-8 \Rightarrow \\ \ \\\Big\{ -3a = 6 \quad si \quad 2a+b = -8\Big\} \Rightarrow \\ \\ \Rightarrow \Big\{ a = -2 \quad si \quad 2\cdot(-2) +b =-8\Big\} \Rightarrow \\ \\ \Rightarrow \Big\{ a = -2 \quad si \quad b = -4\Big\}$

$\Rightarrow \boxed{f(x) = -2x-4}$