已知f(loga(底数）x(真数））=[a(x^2-1)]/[x(a^2-1)],求f(x)解析式.

题目

已知f(loga(底数）x(真数））=[a(x^2-1)]/[x(a^2-1)],求f(x)解析式.

答案

设log(a)x=t,则x=a^t,代入,得f(t)=[a(a^2t-1)]/[a^t(a^2-1)]=(a^2t+1-a)/(a^t+2-a^t),将log(a)x代替t所以
f(x)=(a^log(a)x+1-a)/(a^log(a)x+2-a^log(a)x)