Is every invertible function monotonic?

Every invertible function is (a) monotonic function (b) constant function (c) identity function (d) not necessarily monotonic function

Is every differentiable function continuous?

Statement-1 : Let f : [1, oo) rarr [1, oo) be a function such that f(x) = x^(x) then the function is an invertible function. Statement-2 : The bijective functions are always invertible .

Is every continuous function differentiable?

Prove that every rational function is continuous.

Let f be an invertible function.Show that the inverse of f^(-1) is f

Show that every polynomial function is continuous.

f(x)=[x] is step-up function.Is it a monotonically increasing function for x in R?

Let f(x) be a function given by f(x) =(x^2+1)/([x]) where [] denotes the greatest interger function .Then f(x) is monotonically