[0,\ \infty )\to [0,\ \infty ) $ and $ f(x)=\frac{x}{1+x}, $ then f is [IIT Screening 2003]
A) One-one and onto
B) One-one but not onto
C) Onto but not one-one
D) Neither one-one nor onto
Correct Answer: B
$ {f}’(x)=\frac{1}{{{(1+x)}^{2}}}>0,,\forall x\in [0,,\infty ) $ and range $ \in [0,,1) $
Þ function is one-one but not onto.
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