# 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**.

November 7, 2010 | Filed Under Math

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