Question

设f(x)=1/(1+2^lgx)+1/(1+4^lgx)+1/(1+8^lgx),则f(x)+f(1/x)=

Answer 1

1/(1+2^lgx）+1/[1+2^(-lgx)]

=[2+2^lgx+2^(-lgx)]/[2+2^lgx+2^(-lgx)]=1,

同理1/(1+4^lgx）+1/[1+4^(-lgx)]=1,

1/(1+8^lgx）+1/[1+8^(-lgx)]=1,

∴f(x)+f(1/x)=1+1+1=3.