If f (x + 2) = f (x) + f (2) then prove that: f (0) = 0 and f (-2) = - f (2)

Question

Mathematics

Tripp Kim

3 January, 06:04

If f (x + 2) = f (x) + f (2) then prove that: f (0) = 0 and f (-2) = - f (2)

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Answers (1)

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Yesenia Goodwin · Answer 1

f (0) = 0,

f (-2) = -f (2)

Step-by-step explanation:

f (x+2) = f (x) + f (2)

1. x=0

f (0+2) = f (0) + f (2)

f (2) = f (0) + f (2)

f (0) = f (2) - f (2) = 0

f (0) = 0

2. x=-2

f (-2+2) = f (-2) + f (2)

f (0) = f (-2) + f (2)

f (0) = 0, f (-2) + f (2) = 0

f (-2) = -f (2)