Question

Let f(x) = x-2/4 and g(x)= 2x^2+4. I already found f(g(x)). Now I need help finding g(f(x)).

Answer 1

f(g(x)) = f(2x^2 + 4) = (2x^2 + 4 - 2)/4 = (2x^2 + 2)/4 = 2(x^2 + 1)/4 =(x^2 + 1)/2 .........now I need g(f(x)).

Answer 2

so far I have gotten g(f(x))= g((x-2)/4)= 2x^2+4(-2/4)= 2x^2+(-8/16)= and I am stuck

Answer 3

@mathstudent55 I opened a new one because the other got confusing and long.

Answer 4

\[f(x)=\frac{x-2}{4}\\
g(x)=2x^2+4\\
\begin{align*}g(f(x))&=g\left(\frac{x-2}{4}\right)\\
&=2\left(\frac{x-2}{4}\right)^2+4\\
&=2\left(\frac{(x-2)^2}{16}\right)+4\\
&=\frac{1}{8}\left(x^2-4x+4\right)+4\\
&=\frac{1}{8}x^2-\frac{1}{2}x+\frac{1}{2}+4\\
&=\frac{1}{8}x^2-\frac{1}{2}x+\frac{9}{2}
\end{align*}\]