👤

Sa se determine functia g:R->R stiind ca:
(f compus cu g)(x)=2x+3 iar f:R->R, f(x)=3x-4.



Răspuns :

notez 0 compunerea
f0g=f(g(x))
deci daca f(x)=3x-4
f0g=2x+3
si notam g(x)=ax+b ⇒
f0g=3(ax+b)-4=2x+3
3ax+3b-4=2x+3
3ax=2x⇒a=2/3
si 
3b-4=3
3b=7⇒b=7/3
atunci
g(x)=2x/3+7/3