当x>1时,求f(x)=x²-3x+1/x+1的值域
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![当x>1时,求f(x)=x²-3x+1/x+1的值域](/uploads/image/z/3757313-65-3.jpg?t=%E5%BD%93x%EF%BC%9E1%E6%97%B6%2C%E6%B1%82f%EF%BC%88x%EF%BC%89%EF%BC%9Dx%26%23178%3B-3x%2B1%EF%BC%8Fx%2B1%E7%9A%84%E5%80%BC%E5%9F%9F)
当x>1时,求f(x)=x²-3x+1/x+1的值域
当x>1时,求f(x)=x²-3x+1/x+1的值域
当x>1时,求f(x)=x²-3x+1/x+1的值域
f(x)=(x^2-3x+1)/(x+1) = (x^2+x-4x-4+5)/(x+1) = x - 4 + 5/(x+1)f'(x) = 1 - 5/(x+1)^2 = { (x+1)^2 - 5 ] / (x+1)^2x>1x∈(1,-1+√5)时,f'(x)<0,f(x)单调减x∈(-1+√5,+∞)时,f'(x)>0,f(x)单调增x=-1+√5时,最小值f(x)min= -1+√5 - 4 + 5/(-1+√5+1) = -5+2√5值域【-5+2√5,+∞)