Function

A function f(x) has the following properties:

i) f(1) = 1
ii) f(2x) = 4f(x) + 6
iii) f(x + 2) = f(x) + 12x + 12

Calculate f(6) !

Solution ?


Solution:

Using property iii) with x = 1,
f(3) = f(1) + 12(1) + 12 = 1 + 12 + 12 = 25
since f(1) = 1 by property i).
Using property ii) with x = 3,
f(6) = 4f(3) + 6 = 4(25) + 6 = 106
Therefore, the value of f(6) is 106.

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