Let f : R → R, such that f’ (0) = 1
and f (x +2y) = f (x) + f (2y) + ex+2y (x + 2y) – x. ex – 2y. e2y + 4xy,
∀ x, y Ïµ R. Find f (x).
If g(x) is continuous function in [0, ∞) satisfying g(1) = 1. If
Let f is a differentiable function such that
Let f : R+ → R satisfies the functional equation
If f’(1) = e, determine f (x).
Let f be a function such that .
ind a and b so that the function:
is continuous at x = 0, find the values of Aand B. Also find f (0).
Determine the form of g(x) = f (f (x)) where f (x) and hence find the point of iscontinuity of g, if any.
Find the natural number a for which where the function f satisfies the relation f (x + y) = f (x) f (y) for all natural number x, y and further f (1) 2.