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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'. If it is known that f(4) + f(5) = 37, then what is the value of f(3) + f(6)?
  • a)
    11
  • b)
    20
  • c)
    31
  • d)
    46
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A function f(x) is defined as f(x) = f(x - 2) + x(x - 2) for all the ...
It is given that f(x) = f(x - 2) + x(x - 2)
Hence substituting x =2, we get f(2) = f(0) + 2.0 or f(2) = f(0).
Similarly by substituting x = 3, and so on, we obtain f(3), f(4), f(5), f(6) as follows:-
f(3) = f(1) + 3.1 = f(1) + 3
f(4) = f(2) + 4.2 = f(2) + 8 = f(0) + 8
f(5) = f(3) + 5.3 = f(3) + 15 = (f(1) +3) + 15 = f(1) + 18
f(6) = f(4) + 6.4 = f(4) + 24 = (f(2) + 8) + 24 = f(2) + 32 = f(0) + 32
Now it is given that f(4) + f(5) = 37
This implies that f(0) + f(1) + 26 = 37 or f(0) + f(1) = 11.
Hence, f(3) + f(6) = f(0) + f(1) + 35 = 11 + 35 = 46
Hence, the correct option is (d).
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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'. If it is known that f(4) + f(5) = 37, then what is the value of f(3) + f(6)?a)11b)20c)31d)46Correct answer is option 'D'. Can you explain this answer?
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