Question

Sejam f e g funções definidas por f(x)=2x+m e g(x)=5x-3, obtenha o valor de m de tal forma que f(g(x))=g(f(x))

Answer 1

$\left\begin{array}{ccc} f(g(x))&=&g(f(x))\\\\\\2\,.\,g(x)~+~m&=&5\,.\,f(x)~-~3\\\\\\2\,.\,(5x-3)+m&=&5\,.\,(2x+m)~-~3\\\\\\10x-6+m&=&10x+5m~-~3\\\\\\m-5m&=&-3+6\\\\\\-4m&=&3\end{array}\right\\\\\\\\~~~~~~~~~~~~~~~~~~\boxed{m~=~-\frac{3}{4}}$