Question

设f(x)关于(1,2)对称,反函数为F-1(X)(这里不为减一),F(4)=0,则F-1(4)=?

Answer 1

设点（x,y)是曲线y=f(x)上任一点.则由题设知,点（2-x,4-y)也在曲线y=f(x）上,故有：y=f(x）,且4-y=f(2-x).===>f(x)+f(2-x)=4.由题意有：f(4)=0,即f(-2)=4,===>F-1(4)=-2.