Question

Fie functiile f,g:R-R ,f(x)= 2x+1,g(x)=cx+d. Determinati c,d €R asa incat (f compus cu g)(x)=x,x€R

Answer 1

f°g(x)=f°(g(x))=2g*x)+1=2(cx+d)+1=x  =>
2*cx+2d+1=x=>
2c=1  =>c=-1/2  si
2d+1=0=>d=-1/2
g(x)=-1/2 x-1/2
g(x)  este  inversa  functiei  f