A function `f` on R into itself is continuous at a point a in R. if `f` for each `egt0`. there exists, `delta gt0` such that `|f(x)-f(a)| < in => |x-a| < delta`

If f(x) is continuous function in [0,2pi] and f(0)=f(2 pi ), then prove that there exists a point c in (0,pi) such that f(x)=f(x+pi).

If f(x) is continuous function in [0,2pi] and f(0)=f(2 pi ), then prove that there exists a point c in (0,pi) such that f(x)=f(x+pi).

If f(x) is continuous function in [0,2pi] and f(0)=f(2 pi ), then prove that there exists a point c in (0,pi) such that f(x)=f(x+pi).

Let f be a function such that f(x+f(y)) = f(x) + y, AA x, y in R , then find f(0). If it is given that there exists a positive real delta such that f(h) = h for 0 lt h lt delta , then find f'(x)

Let f be a function such that f(x+f(y)) = f(x) + y, AA x, y in R , then find f(0). If it is given that there exists a positive real delta such that f(h) = h for 0 lt h lt delta , then find f'(x)

Let f be a function such that f(x+f(y)) = f(x) + y, AA x, y in R , then find f(0). If it is given that there exists a positive real delta such that f(h) = h for 0 lt h lt delta , then find f'(x)

Let f be a function such that f(x+f(y)) = f(x) + y, AA x, y in R , then find f(0). If it is given that there exists a positive real delta such that f(h) = h for 0 lt h lt delta , then find f'(x)

f: R to R is a continuous and f(x)=int_(0)^(x)f(t)dt then f(log_(e)5)= ?