Let f : (0, ∞) → R be defined by f(x) = ln x. Prove that f is onto.
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Let f : (0, ∞) → R be defined by f(x) = ln x. Prove that f is onto.
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- Prove that if a subring R of an integral domain D contains the unity element of D, then R is an integral domain. [Type here][Type here]Let where is a field and let . Prove that if is irreducible over , then is irreducible over .For an element x of an ordered integral domain D, the absolute value | x | is defined by | x |={ xifx0xif0x Prove that | x |=| x | for all xD. Prove that | x |x| x | for all xD. Prove that | xy |=| x || y | for all x,yD. Prove that | x+y || x |+| y | for all x,yD. Prove that | | x || y | || xy | for all x,yD.
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