Question

Se f(x)= 3x+5 e h(x)=3x²+3x+2, encontre a função g(x) tal que fog=h

Answer 1

$f[g(x)]=h(x)=3x^2+3x+2\\f[g(x)]=3[g(x)]+5\\3g(x)+5=3x^2+3x+2\\3g(x)=3x^2+3x+2-5\\g(x)=\frac{3x^2+3x-3}{3}=\boxed{x^2+x-1}$