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Questions › DSE › DSE 2010 › Q40
2 marksMathematics › Sets, relations and functions › One-to-one, onto and invertible functionsHardabout 4 min

DSE 2010 Question 40: Sets, relations and functions

Suppose f:[0,1]→[0,1]f:[0,1]\to[0,1]f:[0,1]→[0,1] is a continuous nondecreasing function with f(0)=0f(0)=0f(0)=0 and f(1)=1f(1)=1f(1)=1. Define g:[0,1]→[0,1]g:[0,1]\to[0,1]g:[0,1]→[0,1] by g(y)=min⁡{x∈[0,1]∣f(x)≥y}g(y)=\min\{x\in[0,1]\mid f(x)\ge y\}g(y)=min{x∈[0,1]∣f(x)≥y}. Then,

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Suppose f:[0,1]→[0,1] is a continuous nondecreasing function with f(0)=0 and f(1)=1. Define g:[0,1]→[0,1] by g(y)=min {x∈[0,1]| f(x)≥ y}. Then, (A) g is non-decreasing (B) If g is continuous, then f is strictly increasing (C) Neither (a) nor (b) is true (D) Both (a) and (b) are true

Also written as: Suppose f:[0,1]->[0,1] is a continuous nondecreasing function with f(0)=0 and f(1)=1. Define g:[0,1]->[0,1] by g(y)=min {x in [0,1]| f(x)>= y}. Then,

Sets, relations and functions has come up 65 times in 6 exams since 2004.

What this question tests

This question is on One-to-one, onto and invertible functions, part of Sets, relations and functions in Mathematics.

Injective, surjective and bijective functions and when an inverse exists.

TestStop has 11 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q13Let f:[0,∞)→ℝ be defined by f(x) = (x+1)/(x+2) for all x in the domain. Then f is
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Question from the DSE 2010 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.