Let f(x) be periodic and k be a positive real number such that f(x+k) + f(x) = 0 for all `x in R` . Prove that f(x) is periodic with period 2k.

Let N be the set of Natural numbers. Consider the function f:NtoN defined by f(x)=x+1, x in N Prove that f is not onto.

Let f(x) = x^2 - 2x + 3 . Then find f (f (x) )

Let f(x) and g(x) be differentiable for 0 le x le 2 such that f(0) = 2, g(0) = 1, and f(2) = 8. Let there exist a real number c in [0, 2] such that f'(c) = 3g'(c) . Then find the value of g(2).

Let R be the set of real numbers. Define the real function. f: R rarr R by f(x)=x+1 0 and sketch the graph of this function.