由题意：f(2)=4a-√2
f(f(2))=f(4a-√2)=a(4a-√2)^2-√2
故a(4a-√2)^2-√2=-√2
即a(4a-√2)^2=0
因为a>0
所以4a-√2=0,a=(√2)/4