Let `f` be any real function and let `g` be a function given by `g(x)=2x` . Prove that `gof=f+f` .

Let the function f: R to R be defined by f(x)=x^(3)-x^(2)+(x-1) sin x and "let" g: R to R be an arbitrary function Let f g: R to R be the function defined by (fg)(x)=f(x)g(x) . Then which of the folloiwng statements is/are TRUE ?

Let f and g be two real valued functions ,defined by f(x) =x ,g(x)=[x]. Then find the value of f+g

Let f,\ g,\ h be real functions given by f(x)=sinx , g(x)=2x and h(x)=cosx . Prove that fog=go(fh)dot

Let f,\ g,\ h be real functions given by f(x)=sinx , g(x)=2x and h(x)=cosx . Prove that fog=go(fh)dot

Let f be a real function. Prove that f(x)-f(-x) is an odd function and f(x)+f(-x) is an even function.

Let f and g be real functions defined by f(x)=(x)/(x+1) and g(x)=(1)/(x+3). Describe the functions gof and fog( if they exist).

Let f(x) = 3x + 8 and g(x) = x^(2) be two real functions. Find (f+g) (x)

Let f(x) = 3x + 8 and g(x) = x^(2) be two real functions. Find (f+g) (x)

Let f and g be real functions defined by f(x)=x/(x+1) a n d g(x)=1/(x+3)dot Describe the functions gof and fog (if they exist).