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B
onto but not one-one
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C
one-one and onto
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D
neither one-one nor onto
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Solution
The correct option is A one-one and into
Given that f:[0,∞)→[0,∞) s.t.f(x)=xx+1 then f′(x)=1+x−x(1+x2)=1(1+x)2 >0,∀x ∴ f is an increasing function ⇒ is one-one. Also Df=[0,∞) And for range let xx+1=y⇒x=yy+1