Question

Why is the answer A? Plz explain.

Answer 1

$\bf f(x)=\cfrac{1}{2}x+a\\\\ -------------------------------\\\\ \stackrel{x=a}{f(a)}=\cfrac{1}{2}(a)+a\implies 3=\cfrac{1}{2}(a)+a\implies 3=\cfrac{a}{2}+a\implies 3=\cfrac{a+2a}{2} \\\\\\ 6=a+2a\implies 6=3a\implies \cfrac{6}{3}=a\implies \boxed{2=a}\\\\ -------------------------------\\\\ f(8)=\cfrac{1}{2}(\stackrel{x}{8})+(\stackrel{a}{2})\implies f(8)=\cfrac{8}{2}+2\implies f(8)=6$