函数y=t/t+1(x∈[-1,1])的值域为

Question

函数y=t/t+1(x∈[-1,1])的值域为

Answer 1

f(x)=x^2-2x+2
=(x-1)^2+1
当t+1<1即t<0时
g(t)=f(t+1)
=(t+1)^2-2(t+1)+2
=t^2+1
当t≤1;t+1≥1即0≤t≤1时
g(t)=f(1)=1
当t>1时
g(t)=f(t)=t^2-2t+2=(t-1)^2+1
故g(t)值域为[1,+∞）