Question

A9) Fie f,g:R->R , f(x)=(m+1)x-3, g(x)=x-n.
Sa se determine m,n ∈ R astfel incat f=$g^{-1}$

Answer 1

f=g^(-1) <=> f(g(x))=g(f(x))=x <=> f(x-n)=g((m+1)x-3)=x <=> (m+1)(x-n)-3=(m+1)x-3-n=x, oricare ar fi x din R.

x=0 => (m+1)*(-n)-3=-3-n=0. => n=-3 => m=0.

Intr-adevar n=-3 si m=0 verifica f(g(x))=g(f(x))=x, oricare ar fi x din R.