Question

fie functia f:r->r,f(x)=ax+b. determinati a,b e R stiind ca 3f(x)+2=3x+5,vxer

Answer 1

f:r->r,f(x)=ax+b
3f(x)+2=3x+5
3(ax+b)+2=3x+5
3ax+3b+2=3x+5
3ax+3b=3x+5-2
3ax+3b=3x+3
a=1
b=1

Answer 2

$f:\mathbb_{R}\rightarrow \mathbb_{R}, \quad f(\text{x}) =a\text{x}+b\\ \\ 3\cdot f(\text{x})+2 = 3\text{x}+5 \\ 3\cdot(a\text{x}+b)+2 = 3\text{x}+5 \\ 3a\text{x}+3b+2 = 3\text{x}+5$

$\Rightarrow \left\{ \begin{array}{c} 3a = 3 \\ 3b+2 = 5 \end{array} \right \Rightarrow \left\{ \begin{array}{c} a = \dfrac{3}{3} \\ 3b = 5 -2\end{array} \right \Rightarrow \left\{ \begin{array}{c} a = \dfrac{3}{3} \\ 3b = 3 \end{array} \right \Rightarrow \left\{ \begin{array}{c} a = 1 \\ b = \dfrac{3}{3} \end{array} \right \Rightarrow \\\Rightarrow \left\{ \begin{array}{c} \boxed{a = 1} \\ \boxed{b = 1}\end{array} \right|$