The functions given are,
[tex]\begin{gathered} f(x)=\frac{1}{4}x+2 \\ g(x)=4x-8 \end{gathered}[/tex]
Firstly, Let us solve for f(g(x))
To resolve this, we will substitute x as 4x - 8 into the function f(x)
[tex]\begin{gathered} f(g(x))=\frac{1}{4}(4x-8)+2 \\ f(g(x))=\frac{1}{4}\times4x+\frac{1}{4}\times-8+2 \end{gathered}[/tex][tex]\begin{gathered} f(g(x))=x-2+2 \\ f(g(x))=x-0=x \\ \therefore f(g(x))=x \end{gathered}[/tex]
Let us now solve for g(f(x))
To resolve this, we will substitute x as 1/4x + 2 into the function g(x)
[tex]\begin{gathered} g(f(x))=4(\frac{1}{4}x+2)-8 \\ g(f(x))=4\times\frac{1}{4}x+4\times+2-8 \\ g(f(x))=x+8-8=x+0=x \\ \therefore g(f(x))=x \end{gathered}[/tex]
Therefore, the result will be
[tex]x[/tex]
