Question

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Answer 1

Answer:

hence the period=8

Step-by-step explanation:

f(x)+f(x+4)=f(x+2)+f(x+6)---------------(1)

putting x=x+2

f(x+2)+f(x+2+4)=f(x+2+2)+f(x+2+6)

f(x+2)+f(x+6)=f(x+4)+f(x+8)-----------------(2)

From Equation(1) and (2) we get

f(x)+f(x+4)=f(x+4)+f(x+8)

f(x)=f(x+8)

hence function returns its value after 8

hence the period=8

===========================

putting x=x+4

f(x+4)+f(x+8)=f(x+6)+f(x+10)

putting x=x+6

f(x+6)+f(x+10)=f(x+8)+f(x+12)

f(x+4)+f(x+8)=f(x+8)+f(x+12)

f(x+12)=f(x+4)

putting x+4=y

f(x+4+8)=f(x+4)

f(y)=f(y+8)

hence the period=8