f(-x)=log4(4^(-x)+1)-kx
=log4[(4^x+1)/4^x]-kx
=log4(4^x+1)-x-kx
=log4(4^x+1)-(k+1)x
=log4(4^x+1)+kx=f(x)
=>-(k+1)=k
=>k=-1/2.