Any function `f:N to R` continuous on N.

Let f (x) be an odd function for continuous at x in R If f(x) is continuous at x = a, prove that it is continous at x=-a

Assertion (A): f(x) = (sin {[ x] pi})/(1 + x^(2)) here [x] denotes greastest integer function, is continuous on R Reason (R) : Every constant function is continuous on R

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer.

f: N to R be any function then show that f is continuous on N .

If f: R rarr R is a function such that f(x +y) =f(x) +f(y) forall x,y in R then f is continuous on R if it is continuous at a single point in R.

Give examples of two functions f : N to N and g : N to N such g o f is onto but f is not onto.