If f : [ 0 , ∞ ) → [ 0 , ∞ ) and f ( x ) = 1 + x x , then f is

Question

If f : [ 0 , ∞ ) → [ 0 , ∞ ) and f ( x ) = 1 + x x ​ , then f is, One-one and onto, One-one but not onto, Onto but not one-one, Neither one-one nor onto

MARKS App · Accepted Answer

f ′ ( x ) = ( 1 + x ) 2 1 ​ > 0 , ∀ x ∈ [ 0 , ∞ ) and range ∈ [ 0 , 1 ) ⇒ function is one-one but not onto.

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