If f:R→R is a function satisfying the propertyf(2x+3)+f(2x+7)=2,∀x∈R, then the period of f(x) is ______

We have f(2x+3)+f(2x+7)=2_______(1)Replace x by x + 1,f(2x+5)+f(2x+9)=2_______(2)Replace x by x + 2,f(2x+7)+f(2x+11)=2_______(3)From (1) and (3)We get f(2x+3)−f(2x+11)=0i.e., f(2x+3=f(2x+11)⇒T=8required period equal to 4