JEE Main 2002 Mathematics question on Sets Relations and Functions
Let function f:R→R be defined by f(x)=2x+sinx for x∈R. Then, f is
A.
one-to-one and onto
B.
one-to-one but not onto
C.
onto but not one-to-one
D.
neither one-to-one nor onto
Show answer and solution
Correct option: A
Solution
f'(x) = 2 + cos x ≥ 2 - 1 = 1 > 0 for all x ∈ R, so f is strictly increasing, hence one-to-one. As x → ±∞, f(x) → ±∞, and f is continuous, so by IVT the range is all of R, making f onto.
[AIEEE 2002]
Practise Sets Relations and Functions the way it is asked
A timed set of real JEE Main Sets Relations and Functions questions, graded as the exam grades. No sign-up.
