Question

函数f(x)=(2-x)/(x-1)的图像是由函数f(x)=(1+x)/x的图像沿位置向量a=(m,n),平移所得,求m

Answer 1

f(x)=(2-x)/(x-1)=-(x-2)/(x-1)

=-[(x-1)-1]/(x-1)

=-1+1/(x-1)

g(x)=(1+x)/x =1+1/x (不能再用f）

g(x)向右平移1个单位,得到y=1+1/(x-1)

y=1+1/(x-1)向下平移2个单位得到f(x)=-1+1/(x-1)

∴向量a=(m,n)即向右1,向下2

∴m=1,n=-2