If f,g,h are real valued function defined on R, then prove that
(f+g)oh=foh+goh. what can you say about fo(g+h)? Justify your answer.

Let f(x) and g(x) are two differentiable functions. If f(x)=g(x) , then show that f'(x)=g'(x) . Is the converse true ? Justify your answer

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

H-7.Let'f' be a real valued function defined for all real numbers x such that for some positive constant 'a' theequation f(x+a)= 2 1 ​ + f(x)−(f(x)) 2 holds for all x. Prove that the function f is periodic.

Assertion: If f, g, h are real valued functions then f(g+h)=fg+fh. Reason: If f,g,h are real valued functions (fg)(x)=f(x) g(x).

Let f be the subset of Z xx Z defined by f={(ab,a+b) : a,b in Z} . Is f a function from Z to Z? Justify your answer.

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___

If f(x)=x^(2), g(x)=3x and h(x)=x-2 . Prove that (fog)oh=fo(goh) .