Defence Exam > Defence Questions > Consider the following statements:Statement 1...
Start Learning for Free
Consider the following statements:
Statement 1 : The function f: IR → IR such that f ( x ) = x3 for all x ∈ IR is one-one.
Statement 2 : f (a) => f (b) for all a, b ∈ IR if the function f is one-one.
Statement 1 : The function f: IR → IR such that f ( x ) = x3 for all x ∈ IR is one-one.
Statement 2 : f (a) => f (b) for all a, b ∈ IR if the function f is one-one.
Q. Which one of the following is correct in respect of the above statements ?
- a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.
- b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.
- c)Statement 1 is true but Statement 2 is false.
- d)Statement 1 is false but Statement 2 is true.
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider the following statements:Statement 1 : The function f: IR&rar...
So it is one-one function
Hence option (a) is correct.
Hence option (a) is correct.
Most Upvoted Answer
Consider the following statements:Statement 1 : The function f: IR&rar...
Analysis of Statement 1
The function f: IR → IR defined by f(x) = x³ is a cubic function. To determine if it is one-one (injective):
- A function is one-one if for any two distinct values a and b in its domain, f(a) ≠ f(b).
- For the function f(x) = x³, if f(a) = f(b), then a³ = b³.
- This implies that a = b, indicating that the function does not map different inputs to the same output.
Thus, Statement 1 is true: f(x) = x³ is indeed a one-one function.
Analysis of Statement 2
Statement 2 asserts that if f(a) = f(b) for all a, b in IR, then the function f is one-one. This statement is actually the definition of a one-one function:
- A function is considered one-one if it never assigns the same value to two different domain elements.
- The condition f(a) = f(b) implies a must equal b, thereby confirming that the function is one-one.
Therefore, Statement 2 is also true.
Correct Relationship Between Statements
- Both statements are true, and Statement 2 serves as a correct explanation for Statement 1.
- Statement 2 highlights the definition of a one-one function, which is satisfied by the function in Statement 1.
In conclusion, the correct answer is option 'A': Both statements are true, and Statement 2 is the correct explanation of Statement 1.
The function f: IR → IR defined by f(x) = x³ is a cubic function. To determine if it is one-one (injective):
- A function is one-one if for any two distinct values a and b in its domain, f(a) ≠ f(b).
- For the function f(x) = x³, if f(a) = f(b), then a³ = b³.
- This implies that a = b, indicating that the function does not map different inputs to the same output.
Thus, Statement 1 is true: f(x) = x³ is indeed a one-one function.
Analysis of Statement 2
Statement 2 asserts that if f(a) = f(b) for all a, b in IR, then the function f is one-one. This statement is actually the definition of a one-one function:
- A function is considered one-one if it never assigns the same value to two different domain elements.
- The condition f(a) = f(b) implies a must equal b, thereby confirming that the function is one-one.
Therefore, Statement 2 is also true.
Correct Relationship Between Statements
- Both statements are true, and Statement 2 serves as a correct explanation for Statement 1.
- Statement 2 highlights the definition of a one-one function, which is satisfied by the function in Statement 1.
In conclusion, the correct answer is option 'A': Both statements are true, and Statement 2 is the correct explanation of Statement 1.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer?
Question Description
Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer?.
Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following statements:Statement 1 : The function f: IR→ IR such that f ( x ) = x3 for all x ∈IR is one-one.Statement 2 : f (a) => f (b) for all a, b ∈IR if the function f is one-one.Q. Which one of the following is correct in respect of the above statements ?a)Both the statements are true and Statement 2 is the correct explanation of Statement 1.b)Both the statements are true and Statement 2 is not the correct explanation of Statement 1.c)Statement 1 is true but Statement 2 is false.d)Statement 1 is false but Statement 2 is true.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup