Question

当X>-1时,求函数fx=x^2-3x+1/x+1的值域

Answer 1

f(x)=[(x+1)(x-4)+5]/(x+1)

=x-4+5/(x+1)

=(x+1)+5/(x+1)-5

x>-1

x+1>0

所以(x+1)+5/(x+1)>=2√[(x+1)*5/(x+1)]=2√5

所以(x+1)+5/(x+1)-5>=2√5-5

值域[2√5-5,+∞)