- f(x)=1/(1+2^lgx)+1/(1+4^lgx)+1/(?
- 1/[1+2^(-lgx)]+1/[1+4^(-lgx)]+1/[1+8^(-lgx)].
求f(x)+f(1/x)的值.
- 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)=3,
∴f(1/x)=3,
∴f(x)+f(1/x)=6.