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CurcubeulMagic
a fost răspuns

Fie f:R-R
f(2x-4)= x+ f2)-f(4)
Calculati f(x)

Răspuns :

f(x)=ax+b
f(2x-4)= a(2x-4)+b
f(2)= 2a+b
f(4)= 4a+b

f(2x-4)= x+ f(2)-f(4)
a(2x-4)+b = x +2a+b+4a+b
2ax-4a+b=x+6a+2b
2ax=x rezulta 2a=1 a= 1/2
-4a+b=6a+2b
-4*1/2+b= 6*1/2+2b
-2+b=3+2b
-5=b
f(x)=ax+b
f(x)= 1/2 *x-5

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