Prove that every function can be expressed as the sum of an -even and an odd function.

Show that any function can be expressed as the sum of an odd function and even function

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

Each question has four choices, a,b,c and d,out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. a) if both the statements are true and statement 2 is the correct explanation of statement 1. b) If both the statements are true but statement 2 is not the correct explanation of statement 1. c) If statement is True and statement2 is false. d) If statement1 is false and statement2 is true. Statement 1: f(x)=(log)_ex cannot be expressed as the sum of odd and even function. Statement 2 : f(x)=(log)_e x in neither odd nor even function.

The function f(x)=(x+1)/(x^3+1) can be written as the sum of an even function g(x) and an odd function h(x) . Then the value of |g(0)| is___________

The graph of the function y=f(x) passing through the point (0,1) and satisfying the differential equation (dy)/(dx)+ycosx=cosx is such that (a) it is a constant function. (b) it is periodic (c) it is neither an even nor an odd function. (d) it is continuous and differentiable for all f(x )

Prove that every rational function is continuous.

Prove that the square of an odd integer can be expressed in the form 8p + 1 where p = 0 or a positive integer.

True or False -The derivative of an even function is always an odd function.

Non functional stomata can be seen in

Prove that the derivative of an odd function an ever function .