If ∫ d x x 2 + x = ln ⁡ f x + C (where C is the constant of integration), then the range of y = f x , ∀ x ∈ R - - 1,0 is

Question

If ∫ d x x 2 + x = ln ⁡ f x + C (where C is the constant of integration), then the range of y = f x , ∀ x ∈ R - - 1,0 is, R - 1, R - 0, R - 0,1, R - 0 , - 1

MARKS App · Accepted Answer

Ι = ∫ d x x x + 1 = ∫ d x x - ∫ d x x + 1 ⇒ Ι = ln ⁡ x - ln ⁡ x + 1 + C = ln ⁡ x x + 1 + C i.e. y = f x = x x + 1 ⇒ y x + y = x ⇒ x = y 1 - y ⇒ y ∈ R - 0,1 as x ≠ 0

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