作业帮已知a>0,a不等于1,f(x)满足f(log aX)=[a(x2-1)]/[x(a2-1)],求解y=f(x）的解析式和奇偶性
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已知a>0,a不等于1,f(x)满足f(log aX)=[a(x2-1)]/[x(a2-1)],求解y=f(x）的解析式和奇偶性
已知a>0,a不等于1,f(x)满足f(log aX)=[a(x2-1)]/[x(a2-1)],求解y=f(x）的解析式和奇偶性
已知a>0,a不等于1,f(x)满足f(log aX)=[a(x2-1)]/[x(a2-1)],求解y=f(x）的解析式和奇偶性
设log ax=y
则x=a^y
代入原式得：
f(y)=[a(a^2y-1]/a^y(a^2-1)]=[a^(1+y)-a^(1-y)]/[a^2-1]
即f(x)=[a^(1+x)-a^(1-x)]/[a^2-1]
又f(-x)=)=[a^(1-x)-a^(1+x)]/[a^2-1]=-f(x)
所以f(x)为奇函数