If is a continuous function ( is the set of real numbers) and is an open subset of , then the set is necessarily
Tap an option to check your answer.
0 marksMathematicsReal analysisTopology of the real line: open, closed and compact setsModerateabout 1 min
DSE 2016 Question 13: Real analysis
Answer and worked solution
Checking your account…
Plain-text version
If f:ℝ→ℝ is a continuous function (ℝ is the set of real numbers) and E is an open subset of ℝ, then the set {x∈ℝ| f(x)∈ E} is necessarily (A) open (B) closed (C) neither open, nor closed (D) open and closed
Also written as: If f:R->R is a continuous function (R is the set of real numbers) and E is an open subset of R, then the set {x in R| f(x) in E} is necessarily
Real analysis has come up 38 times in 5 exams since 2005.
What this question tests
This question is on Topology of the real line: open, closed and compact sets, part of Real analysis in Mathematics.
Which sets are open, closed or compact and how unions and intersections behave.
TestStop has 29 past-paper questions on this subtopic.
Similar questions from other papers
- Match List-I (Types of Interval for variable x) with List-II (Mathematical Representation, given a,b ∈ ℝ with b>a): List-I: (A) Closed Interval; (B) Open Interval; (C)…
- Consider the following statements: (A) The union of a finite number of closed sets is a closed set. (B) The empty set is an open set but not a closed set. (C) Every…
- Consider an economy with 2-goods. The set of all possible positive relative prices is given as: P = {(p₁, p₂) | p₁, p₂ > 0, and p₁ + p₂ = 1}. Identify the correct…
- Consider set X = {1/n | n is a natural number}. Then X is a,
- Let ℝ be the set of real numbers. A subset E of ℝ is said to be open if, for every x ∈ E, there exists r > 0 such that (x - r, x + r) is a subset of E. Then,
Question from the DSE 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.