If f:R→R is a continuous function and satisfies f(x)=f(2x+1), then its not to hard to show that f is a constant.
My question is suppose f is continuous and it satisfies f(x)=f(2x+1), then can the domain of f be restricted so that f doesn't remain a constant. If yes, then give an example of such a function.
Answer
Let f have value 1 on [0,∞) and value 0 on (−∞,−1]. This function is not constant (although it is locally constant), and satisfies f(x)=f(2x+1) whenever x is in its domain.
No comments:
Post a Comment