(1+t)/(t^2-2t+1),t>1且t≠0,的值域怎么求应该是t>0且t≠1

Question

(1+t)/(t^2-2t+1),t>1且t≠0,的值域怎么求
应该是t>0且t≠1

Answer 1

(t+1)/(t²-2t+1)=(t+1)/(t-1)²t>1 t+1>0 t-1>0令f(t)=(t²-2t+1)/(t+1)f(t)=(t²+t-3t-3+4)/(t+1)=[t(t+1)-3(t+1)+4]/(t+1)=t-3+4/(t+1)=t+1+4/(t+1)-4由均值不等式得t+1+4/(t+1)>4f(x)>0函数的值...