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Question

If f(x)+f(x+4)=f(x+2)+f(x+6)xϵ R and a>0 and f(x) is periodic, then period of f(x), is


A
1000
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B
100
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C
10000
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D
10
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Solution

The correct option is A 1000
f(x)+f(x+4)=f(x+2)+f(x+6)...1(i).
Replacing x by x + 2 in equation (i), we get
F(x+2)+f(x+6)=f(x+4)+f(x+8)        . . . . .(ii)
Adding (i) and (ii) f(x)=f(x+8)
f(5)=f(13)=10
f(13)=f(21)=10..
f(805)=10
 100
f(5+8r)=f(13)+f(21)+...+f(805)
r=1
=10+10+....100 times.=10 × 100=1000

Mathematics

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