Matematică
predoiflory
2015-11-12 09:13:15
fie functia f:r->r,f(x)=ax+b. determinati a,b e R stiind ca 3f(x)+2=3x+5,vxer
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dana1
2015-11-12 14:20:32

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

ceaknoris
2015-11-12 14:21:47

[latex]f:mathbb_{R} ightarrow mathbb_{R}, quad $ $f( ext{x}) =a ext{x}+b\ \ 3cdot f( ext{x})+2 = 3 ext{x}+5 \ 3cdot(a ext{x}+b)+2 = 3 ext{x}+5 \ 3a ext{x}+3b+2 = 3 ext{x}+5[/latex] [latex]Rightarrow left{ egin{array}{c} 3a = 3 \ 3b+2 = 5 end{array} ight Rightarrow left{ egin{array}{c} a = dfrac{3}{3} \ 3b = 5 -2end{array} ight Rightarrow left{ egin{array}{c} a = dfrac{3}{3} \ 3b = 3 end{array} ight Rightarrow left{ egin{array}{c} a = 1 \ b = dfrac{3}{3} end{array} ight Rightarrow \Rightarrow left{ egin{array}{c} oxed{a = 1} \ oxed{b = 1}end{array} ight|[/latex]

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