Answer :
[tex]f(x)=x^2[/tex]
Given the point:
[tex]\begin{gathered} (2,1) \\ x=2,g(2)=1 \\ so\colon \\ g(2)=ax^2=1 \\ a(2^2)=1 \\ solve_{\text{ }}for_{\text{ }}a\colon \\ a=\frac{1}{2^2}=\frac{1}{4} \end{gathered}[/tex]Therefore:
[tex]g(x)=(\frac{1}{2}x)^2[/tex]