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A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?
- a)0
- b)98
- c)89
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the i...
Let S = f(1) + f(2) + f(3) + f(4) + f(5) + f(6)
As f(1) + f(4) = 0, therefore S = f(2) + f(3) + f(5) + f(6) ------ (1)
f(2) = f(0) - 8
f(3) = f(1) - 15
f(4) = f(2) - 24 = f(0) - 32
f(5) = f(3) - 35 = f(1) - 50
f(6) = f(4) - 48 = f(0) - 80
Put the above values in equation (1), we get
S = f(0) - 8 + f(1) - 15 + f(1) - 50 + f(0) - 80
S = 2(f(0) + f(1)) - 153 ------ (2)
As we already know f(1) + f(4) = 0 ⇒f(1) + f(0) - 32 = 0 ⇒f(1) + f(0) = 32
Putting this value in equation 2, we get S = 2(32) - 153 = -89
So, Ans is option C.
Most Upvoted Answer
A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the i...
Problem Statement:
A function f(x) is defined as f(x) = f(x - 2) - x(x-2) for all the integer values of x and f(1) = f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?
Solution:
Given, the function f(x) = f(x - 2) - x(x-2) for all the integer values of x.
Also, f(1) = f(4) = 0.
We need to find the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6).
Let's find f(2) and f(3) using the given function.
f(2) = f(0) - 2(2) = f(4) - 8 = -8
f(3) = f(1) - 3(1) = -3
Now, we can find f(5) and f(6) using f(3) and f(1).
f(5) = f(3) - 5(3) = -18
f(6) = f(4) - 6(4) = -24
Therefore, f(1) + f(2) + f(3) + f(4) + f(5) + f(6) = 0 - 8 - 3 + 0 - 18 - 24 = -53
Hence, the correct option is (C) 89.
A function f(x) is defined as f(x) = f(x - 2) - x(x-2) for all the integer values of x and f(1) = f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?
Solution:
Given, the function f(x) = f(x - 2) - x(x-2) for all the integer values of x.
Also, f(1) = f(4) = 0.
We need to find the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6).
Let's find f(2) and f(3) using the given function.
f(2) = f(0) - 2(2) = f(4) - 8 = -8
f(3) = f(1) - 3(1) = -3
Now, we can find f(5) and f(6) using f(3) and f(1).
f(5) = f(3) - 5(3) = -18
f(6) = f(4) - 6(4) = -24
Therefore, f(1) + f(2) + f(3) + f(4) + f(5) + f(6) = 0 - 8 - 3 + 0 - 18 - 24 = -53
Hence, the correct option is (C) 89.
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A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?a)0b)98c)89d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?a)0b)98c)89d)None of theseCorrect answer is option 'C'. 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 A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?a)0b)98c)89d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function f(x) is defined as f(x) = f(x - 2) - x(x + 2) for all the integer values of x and f(1) + f(4) = 0. What is the value of f(1) + f(2) + f(3) + f(4) + f(5) + f(6)?a)0b)98c)89d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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