Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2016 › Q20
0 marksMathematics › Limits, continuity and differentiability › Continuity and discontinuitiesHardabout 3 min

DSE 2016 Question 20: Limits, continuity and differentiability

g:R→[0,1]g:\mathbb{R}\to[0,1]g:R→[0,1] is a non-decreasing and right continuous step function such that g(x)=0g(x)=0g(x)=0 for all x≤0x\le0x≤0 and g(x)=1g(x)=1g(x)=1 for all x≥1x\ge1x≥1. Let us define g−1g^{-1}g−1 as follows: g−1(y)=inf⁡{x≥0∣g(x)≥y}g^{-1}(y)=\inf\{x\ge0\mid g(x)\ge y\}g−1(y)=inf{x≥0∣g(x)≥y}. Which of the following is true about g−1g^{-1}g−1:

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

g:ℝ→[0,1] is a non-decreasing and right continuous step function such that g(x)=0 for all x≤0 and g(x)=1 for all x≥1. Let us define g⁻¹ as follows: g⁻¹(y)=inf {x≥0| g(x)≥ y}. Which of the following is true about g⁻¹: (A) is a continuous function (B) is right-continuous but not left continuous (C) is left-continuous but not right continuous (D) neither left-continuous nor right-continuous

Also written as: g:R->[0,1] is a non-decreasing and right continuous step function such that g(x)=0 for all x<=0 and g(x)=1 for all x>=1. Let us define g^(-1) as follows: g^(-1)(y)=inf {x>=0| g(x)>= y}. Which of the following is true about g^(-1):

Limits, continuity and differentiability has come up 122 times in 7 exams since 2006.

What this question tests

This question is on Continuity and discontinuities, part of Limits, continuity and differentiability in Mathematics.

When a function is continuous at a point and what kinds of breaks occur.

TestStop has 20 past-paper questions on this subtopic.

Practise Limits, continuity and differentiabilityMore on Continuity and discontinuities

Similar questions from other papers

  • CUET-PG 2026 · Q24Derivative of Average cost (AC) = 5 + 2/Q is
  • IIT JAM 2026 · Q50The value of the first derivative of f(x)=(3x³+2x²+x+1)² evaluated at x=2 is (*in integer*).
  • UGC-NET 2026 · Q8What will be the third derivative of the following rational function? y = g(x) = x/(1+x); (x ≠ -1)
  • CUET-PG 2025 · Q3The exports of goods of a country, G = G(t) has a growth rate of a/t, and its exports of services, S = S(t) has a growth rate of b/t. What is the growth rate of its…
  • GATE 2025 · Q32Let f(x) = -3x²(1-x) - 3x(1-x)² - (1-x)³. Then, df(x)/dx =

Question from the DSE 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.