Question

a>0且a≠1,f(log aX)=a/(a/(a^2-1)(x-1/x)),求f(x)

Answer 1

在f(log aX)=a/(a/(a^2-1)(x-1/x)) 中,设log aX=t,则a^t=x,所以f(log aX)=a/(a/(a^2-1)(x-1/x)) 可化为f(t)=a/[a/(a^2-1)(a^t-1/a^t)] =(a^2-1)(a^t-1/a^t)

所以f(x) =(a^2-1)(a^x-1/a^x)