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Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1)F(x–2)F(x–3)F(x–4) for all x ≥ 0.Given the values of If F (83) = 81 and F(77) = 9, then the value of F(102) equals to
- a)27
- b)54
- c)729
- d)Data Insufficient
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1...
Solution:
Given, F(x) F(x 1) = F(x 1)F(x2)F(x3)F(x4) for all x 0.
We need to find the value of F(102).
Let's try to simplify the given equation by substituting x = 77, 78, 79...82.
F(77) F(78) = F(78) F(79) F(80) F(81)
F(78) F(79) = F(79) F(80) F(81) F(82)
F(79) F(80) = F(80) F(81) F(82) F(83)
Now, we can cancel the common terms from the above equations.
F(77) = F(82) F(81) F(80)
F(78) = F(83) F(82) F(81)
Substituting the given values of F(77) and F(83), we get:
9 = F(82) x 81 x F(80)
81 = F(83) x F(82) x 81
Dividing the above two equations, we get:
F(82) x F(80) = 9
Hence, we can write:
F(77) = 9 x F(81)
F(78) = 81 x F(81)
Again, substituting the given values of F(77) and F(83), we get:
9 x F(81) = F(82) x 81 x F(80)
F(82) x F(80) = 9
Therefore, we can write:
F(81) x F(82) x F(80) = 81
F(81) x 9 = 81
F(81) = 9
Now, substituting F(81) in the equation F(78) = 81 x F(81), we get:
F(78) = 729
Finally, substituting F(78) and F(81) in the equation F(77) = 9 x F(81), we get:
F(77) = 81
Hence, we can conclude that the given data is insufficient to find the value of F(102).
Given, F(x) F(x 1) = F(x 1)F(x2)F(x3)F(x4) for all x 0.
We need to find the value of F(102).
Let's try to simplify the given equation by substituting x = 77, 78, 79...82.
F(77) F(78) = F(78) F(79) F(80) F(81)
F(78) F(79) = F(79) F(80) F(81) F(82)
F(79) F(80) = F(80) F(81) F(82) F(83)
Now, we can cancel the common terms from the above equations.
F(77) = F(82) F(81) F(80)
F(78) = F(83) F(82) F(81)
Substituting the given values of F(77) and F(83), we get:
9 = F(82) x 81 x F(80)
81 = F(83) x F(82) x 81
Dividing the above two equations, we get:
F(82) x F(80) = 9
Hence, we can write:
F(77) = 9 x F(81)
F(78) = 81 x F(81)
Again, substituting the given values of F(77) and F(83), we get:
9 x F(81) = F(82) x 81 x F(80)
F(82) x F(80) = 9
Therefore, we can write:
F(81) x F(82) x F(80) = 81
F(81) x 9 = 81
F(81) = 9
Now, substituting F(81) in the equation F(78) = 81 x F(81), we get:
F(78) = 729
Finally, substituting F(78) and F(81) in the equation F(77) = 9 x F(81), we get:
F(77) = 81
Hence, we can conclude that the given data is insufficient to find the value of F(102).
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Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1...
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Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1)F(x–2)F(x–3)F(x–4) for all x ≥ 0.Given the values of If F (83) = 81 and F(77) = 9, then the value of F(102) equals toa)27b)54c)729d)Data InsufficientCorrect answer is option 'A'. Can you explain this answer?
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Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1)F(x–2)F(x–3)F(x–4) for all x ≥ 0.Given the values of If F (83) = 81 and F(77) = 9, then the value of F(102) equals toa)27b)54c)729d)Data InsufficientCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1)F(x–2)F(x–3)F(x–4) for all x ≥ 0.Given the values of If F (83) = 81 and F(77) = 9, then the value of F(102) equals toa)27b)54c)729d)Data InsufficientCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1)F(x–2)F(x–3)F(x–4) for all x ≥ 0.Given the values of If F (83) = 81 and F(77) = 9, then the value of F(102) equals toa)27b)54c)729d)Data InsufficientCorrect answer is option 'A'. Can you explain this answer?.
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