. If f(x+8)=f(x)+f(8) then prove that: f(0)=0 and f(-8)=-f(8).

asked Jan 16, 2022 6.0k views

1 vote

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4 votes

Explanation:

Given

The equation is
f(x+8)=f(x)+f(8)

Substitute 0 for x

$\Rightarrow f(0+8)=f(0)+f(8)\\\Rightarrow f(0)=f(8)-f(8)\\\Rightarrow f(0)=0$

Now, substitute
for

$\Rightarrow f(-8+8)=f(-8)+f(8)\\\Rightarrow f(0)=f(-8)+f(8)\\\Rightarrow 0=f(-8)+f(8)\\\Rightarrow f(-8)=-f(8)$

Hence proved

Kukuh Tw answered Jan 22, 2022

4.3k points

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