设f^-1(x)是函数f(x)=loga(x+1)的反函数,若(1+f^-1(a))乘以(1+f^-1(b)=5,则f(a+b)的值
问题描述:
设f^-1(x)是函数f(x)=loga(x+1)的反函数,若(1+f^-1(a))乘以(1+f^-1(b)=5,则f(a+b)的值
答
f^-1(x) = a^x - 1
(1+f^-1(a))*(1+f^-1(b)) = a^a * a^b = a^(a+b) = 5
=>
f^-1(a+b) = a^(a+b) -1 = 4