To find the composition we need, let's first find the general expression:
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(2x-1) \\ =(2x-1)^2+1 \\ =4x^2-4x+1+1 \\ =4x^2-4x+2 \end{gathered}[/tex]Hence:
[tex](g\circ f)(x)=4x^2-4x+2[/tex]Now we can evaluate when x=1/2:
[tex]\begin{gathered} (g\circ f)(\frac{1}{2})=4(\frac{1}{2})^2-4(\frac{1}{2})+2 \\ =4(\frac{1}{4})-2+2 \\ =1-2+2 \\ =1 \end{gathered}[/tex]Therefore:
[tex](g\circ f)(\frac{1}{2})=1[/tex]