设函数y=f(x)有反函数y=f-1(x)且y=f(x+3)与y=f-1(x-5)互为反函数,求f-1(5)-f-1(0)的值
问题描述:
设函数y=f(x)有反函数y=f-1(x)且y=f(x+3)与y=f-1(x-5)互为反函数,求f-1(5)-f-1(0)的值
答
由y=f(x+3)得x+3=f-(y)
y+3=f-(x)
y=f-(x)-3=f-(x-5)
f-(5)-3=f-(5-5)=f-(0)
f-(5)-f-(0)=3