A function is defined as

f(x+2) = 3 + f(x) when x is even

f(x+2) = x + f(x) when x is odd

f(x+2) = 3 + f(x) when x is even

f(x+2) = x + f(x) when x is odd

f(1) = 4 and f(2) = 3

Find f(f(f(1))) + f(f(f(2)))

Answer: 17

Explanation:

f(f(f(1))) + f(f(f(2))) = f(f(4)) + f(f(3))

Now f(4) can be found by using the definition of the function when x is even. Take x = 2.

f(2+2) = 3 + f(2)

f(4) = 3 + 3

f(4) = 6

Likewise, f(3) can be found by using the definition of the function when x is odd. Take x = 1.

f(1+2) = 1 + f(1)

f(3) = 1 + 4

f(3) = 5

Therefore, f(f(4)) + f(f(3)) = f(6) + f(5)

Again, take x = 4.

f(4+2) = 3 + f(4)

f(6) = 3 + 6

f(6) = 9

Take x = 3.

f(3+2) = 3 + f(3)

f(5) = 3 + 5

f(5) = 8.

Hence f(6) + f(5) = 9 + 8 = 17.

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