Question

Sendo f(g(x)) = 4x+3 e g(x) = 2x-1 determine f(x):

Answer 1

$\begin{matrix}f[g(x)]=4x+3\\\\\\\\\\\\\\\end{matrix}\qquad\qquad\qquad\qquad\qquad\begin{matrix}{g}(x)=2x-1\\\\2x-1=g(x)\\\\2x=g(x)+1\\\\x=\dfrac{g(x)+1}{2}\end{matrix}\\\\\\f(x)=4\left(\dfrac{g(x)+1}{2}\right)+3\\\\f(x)=2(g(x)+1)+3\\\\f(x)=2g(x)+2+3\\\\f(x)=2g(x)+5\\\\\therefore\ \boxed{f(x)=2x+5}$