Question

dadas as funcoes reais g(x)=3x-2 e f(g(x))=9x2(quadrado)-3x+1, determine f(x).

Answer 1

g(x)=3x-2
f(g(x))=f(3x-2)
9x^2-3x+1=f(3x-2)

fazendo 3x-2=a, teremos
x=(a+2)/3

substituindo, teremos


9[(a+2)/3]^2-3[(a+2)/3]+1=f(a)

f(a)=a^2+3a+3

portanto
f(x)=x^2+3x+3