39period is 8
take 2x+3=t and cntinue
if f: R-R is a function satisfying the property f(2x+3) + f(2x+7) = 2 for all x belongs to R , then the period of f(x) is
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6 Answers
62f(2x+3) + f(2x+7) = 2
put x=x+2 to get
f(2x+7)+f(2x+11)=2
subtract the two equations to get
f(2x+3)=f(2x+11)
put x=x-1.5
to get
f(2x)=f(2x+8)
f(2x)=f(2(x+4))
so the period is 4...
1although i am able to do such kind of problems but i still do not know what is the basis of approach.... is it a mere hit and trial one or is there something to look after????
1you have to look some basic thing. like which part should be vanished to solve the problem................ nishant method was very good.. i also solve problem in this method........................ that method is very much easy and you can definitely get the result................ you first have to vanish constant part and one function .. so that you find two equation............................................................ then solve this ina easy manner..............................
thanks......................
1@ Nishant Sir
u have found the period of f(2x) = 4
but in the ques , it's abt period of f(x) ,
so the answer will be 8 .
nice approach btw !
