The given functions are
[tex]\begin{gathered} f(x)=2^z \\ g(x)=2x+1 \end{gathered}[/tex]First, we have to find the composite function
[tex](f\circ g)(x)[/tex]We have to enter g(x) inside f(x), as follows
[tex](f\circ g)(x)=2^{(2x+1)}[/tex]Now, we evaluate this composition when x = 0.
[tex](f\circ g)(0)=2^{(2(0)+1)}=2^1=2[/tex]Now, we find the second composition, this time we have to enter f(x) inside g(x).
[tex](g\circ f)(x)=2(2^x)+1[/tex]We evaluate the composition when x = 2.
[tex](g\circ f)(2)=2(2^2)+1=2(4)+1=8+1=9[/tex]