Question

已知函数y=(1+bx)/(ax+1) (a>0,x=/-1/a)的图像关于直线y=x对称.

Answer 1

y=(1+bx)/(ax+1);

对称于y=x:x=(1+by)/(ay+1)

axy+y=1+bx;axy+x=1+by

y-x=-b(y-x);b=-1

令A(x1,y1),B(x2,y2);

e1=向量AB=(x2-x1,y2-y1)=(x2-x1,[(a+1)/(ax2+1)(ax1+1)]*(x2-x1))

e2=(1,0)

(x2-x1)*0-[(a+1)/(ax2+1)(ax1+1)]*(x2-x1)*1不等于0

e2于向量AB不共线；

向量c=λ1e1+λe2