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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.
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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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