JEE Main 2003 Mathematics question on Sets Relations and Functions
If f:[0,∞)→[0,∞) and f(x)=1+xx, then f is \hfill
A.
one-one and onto
B.
one-one but not onto
C.
onto but not one-one
D.
neither one-one nor onto
Show answer and solution
Correct option: B
Solution
f'(x) = 1/(1+x)² > 0 for all x ≥ 0, so f is strictly increasing, hence one-one. The range of f is [0, 1) since x/(1+x) → 1 as x → ∞ but never reaches 1, while the codomain is [0, ∞). Since 1 ∈ [0, ∞) has no preimage, f is not onto.
[AIEEE 2003]
Practise Sets Relations and Functions the way it is asked
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