Question

If f(x+4) = f(x) + f(4), XE R, prove that f(0) = 0 and f(-4) = f(4).​

Answer 1

Answer:

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Answer 2

Answer:

solň:- here,

if X=0 then,

f(0+4)= f(0)+f(4)

=> f(4)= f(0)+f(4)

=> f(0)=f(4)-f(4)

=> f(0)= 0——

Again,

if X=(-4) then,

f(-4+4)=f(-4)+f(4)

=> f(0) = f(-4)+f(4)

=> 0= f(-4)+f(4)

=>f(-4)= -f(4)

Now,

if X=4 then,

f(4+4)= f(4)+f(4)

=>f(8)=2.f(4)

=>f(8)-2.f(4)=0

=>f(8)+[-2.f(4)]=O

=>f(8)+2.[-f(4)]=0

=>f(8)+2.f(-4)=0

Hence proved...