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February 03, 2022 • 10:09 am 30 points
• IIT JAM
• Mathematics (MA)

# Let a, b e r and a < b. which of the following statement(s) is/are true? there exists a continuous function f [a,b] > (a, b) such that f is one-one (a) (b) ther

Let a, b e R and a < b. Which of the following statement(s) is/are true? There exists a continuous function f [a,b] > (a, b) such that f is one-one (A) (B) There exists a continuous function f: [a,b]> (a, b) such that f is onto (C) There exists a continuous functionf: (a,b) » [a, b] such that f is one-one (D) There exists a continuous function f (a,b) [a, b] such that f is onto

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• ##### Piyush pachauri

Option A C are correct. For A , just take any one one function to a compact subset of (a,b) For C , Take f = x

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