Let `f(x)=1+x^(2)`. Find a function `g(x)` so that `f(f(x))=1+x^(2)-2x^(3)+x^(4)` .

Let f(x) be a function such that f(x)*f(y)=f(x+y),f(0)=1,f(1)=4. If 2g(x)=f(x)*(1-g(x))

Let g(x) be the inverse of the function f(x) and f'(x)=(1)/(1+x^(3)) then g'(x) equals

Let f(x)=[x] and g(x)=|x| . Find (f+2g)(-1)

Let f(x)=x^(2) and g(x)=2x+1 be two real functions.Find (f+g)(x)(f-g)(x),(fg)(x),((f)/(g))(x)

Let f and g be two differential functions such that f(x)=g'(1)sin x+(g''(2)-1)xg(x)=x^(2)-f'((pi)/(2))x+f''((-pi)/(2))

Let g(x) be the inverse of the function f(x) ,and f'(x) 1/(1+ x^(3)) then g(x) equals

Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=(2x^(2)+3x)g(x) for all x, where g(x) is continuous and g(0)=3 . Then find f'(x) .