Quant Exam > Quant Questions > f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = ...
Start Learning for Free
f1 (x) = x 0 ≤ x ≤ 1
= 1 x ≥ 1
= 0 otherwise
= 1 x ≥ 1
= 0 otherwise
f2 (x) = f1(–x) for all x
f3 (x) = –f2(x) for all x
f4 (x) = f3(–x) for all x
How many of the following products are necessarily zero for every x:
f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1...
We have to consider positive and negative numbers for all the cases.
f1(x) is positive for positive numbers, and 0 for negative numbers. (0 for x = 0)
f2(x) is 0 for positive numbers, and positive for negative numbers. (0 for x = 0)
f3(x) is 0 for positive numbers, and negative for negative numbers. (0 for x = 0)
f4(x) is negative for positive numbers, and 0 for negative numbers. (0 for x = 0)
So, we see that, out of the 3 products in the question, f1(x) * f2(x) and f2(x) * f4(x) are always zero, for any x.
f1(x) is positive for positive numbers, and 0 for negative numbers. (0 for x = 0)
f2(x) is 0 for positive numbers, and positive for negative numbers. (0 for x = 0)
f3(x) is 0 for positive numbers, and negative for negative numbers. (0 for x = 0)
f4(x) is negative for positive numbers, and 0 for negative numbers. (0 for x = 0)
So, we see that, out of the 3 products in the question, f1(x) * f2(x) and f2(x) * f4(x) are always zero, for any x.
Second sub question, f4(x) = f3(-x) = -f2(-x) = -f1(x).
Hence, 1st option is false.
–f3(-x) = f2(-x) = f1(x). Hence this is true.
Hence, 1st option is false.
–f3(-x) = f2(-x) = f1(x). Hence this is true.
0
Most Upvoted Answer
f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1...
We have to consider positive and negative numbers for all the cases.
f1(x) is positive for positive numbers, and 0 for negative numbers. (0 for x = 0)
f2(x) is 0 for positive numbers, and positive for negative numbers. (0 for x = 0)
f3(x) is 0 for positive numbers, and negative for negative numbers. (0 for x = 0)
f4(x) is negative for positive numbers, and 0 for negative numbers. (0 for x = 0)
So, we see that, out of the 3 products in the question, f1(x)*f2(x) and f2(x)*f4(x) are always zero, for any x.
f1(x) is positive for positive numbers, and 0 for negative numbers. (0 for x = 0)
f2(x) is 0 for positive numbers, and positive for negative numbers. (0 for x = 0)
f3(x) is 0 for positive numbers, and negative for negative numbers. (0 for x = 0)
f4(x) is negative for positive numbers, and 0 for negative numbers. (0 for x = 0)
So, we see that, out of the 3 products in the question, f1(x)*f2(x) and f2(x)*f4(x) are always zero, for any x.
Free Test
FREE
| Start Free Test |
Community Answer
f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1...
Products of Functions Explanation:
Product f1(x) f2(x):
- f1(x) = 1 for 0 ≤ x ≤ 1 and f2(x) = f1(–x)
- When x is in the range 0 ≤ x ≤ 1, f1(x) = 1 and f2(x) = f1(–x) = 1
- Therefore, f1(x) f2(x) = 1 * 1 = 1, not necessarily zero for every x
Product f2(x) f3(x):
- f2(x) = f1(–x) and f3(x) = –f2(x)
- Substituting f2(x) into f3(x), we get f3(x) = –f1(–x)
- When x is in the range 0 ≤ x ≤ 1, f2(x) = f1(–x) = 1 and f3(x) = –f1(–x) = –1
- Therefore, f2(x) f3(x) = 1 * –1 = –1, not necessarily zero for every x
Product f2(x) f4(x):
- f2(x) = f1(–x) and f4(x) = f3(–x)
- Substituting f3(–x) into f4(x), we get f4(x) = f3(–(–x)) = f3(x) = –f2(x)
- Therefore, f2(x) f4(x) = f1(–x) * –f2(x) = 1 * (–1) = –1, not necessarily zero for every x
Conclusion:
- Out of the given products, only f2(x) f3(x) and f2(x) f4(x) are necessarily zero for every x.
Product f1(x) f2(x):
- f1(x) = 1 for 0 ≤ x ≤ 1 and f2(x) = f1(–x)
- When x is in the range 0 ≤ x ≤ 1, f1(x) = 1 and f2(x) = f1(–x) = 1
- Therefore, f1(x) f2(x) = 1 * 1 = 1, not necessarily zero for every x
Product f2(x) f3(x):
- f2(x) = f1(–x) and f3(x) = –f2(x)
- Substituting f2(x) into f3(x), we get f3(x) = –f1(–x)
- When x is in the range 0 ≤ x ≤ 1, f2(x) = f1(–x) = 1 and f3(x) = –f1(–x) = –1
- Therefore, f2(x) f3(x) = 1 * –1 = –1, not necessarily zero for every x
Product f2(x) f4(x):
- f2(x) = f1(–x) and f4(x) = f3(–x)
- Substituting f3(–x) into f4(x), we get f4(x) = f3(–(–x)) = f3(x) = –f2(x)
- Therefore, f2(x) f4(x) = f1(–x) * –f2(x) = 1 * (–1) = –1, not necessarily zero for every x
Conclusion:
- Out of the given products, only f2(x) f3(x) and f2(x) f4(x) are necessarily zero for every x.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer?
Question Description
f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer?.
f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer?.
Solutions for f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice f1 (x) = x 0 ≤ x ≤ 1 = 1 x ≥ 1 = 0 otherwisef2 (x) = f1(–x) for all xf3 (x) = –f2(x) for all xf4 (x) = f3(–x) for all xHow many of the following products are necessarily zero for every x:f1(x) f2 (x), f2 (x) f3 (x), f2(x) f4 (x)a)0b)1c)2d)3Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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