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(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

Let f(x)=sqrtx and g(x)=x be two functions defined over the set of non-negative real numbers. Find (f+g) (x), (f-g), (fg) (x) and (f/g) (x) .

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(x) and g(x) be real valued functions such that f(x)g(x)=1, AA x in R."If "f''(x) and g''(x)" exists"AA x in R and f'(x) and g'(x) are never zero, then prove that (f''(x))/(f'(x))-(g''(x))/(g'(x))=(2f'(x))/(f(x))

Let f(x)=x^(3)+x+1 and let g(x) be its inverse function then equation of the tangent to y=g(x) at x = 3 is

If f(x) =x^(2) -2,g (x) =2x+ 1 then f^(@) g (x)

Let f(x)a n dg(x) be two continuous functions defined from RvecR , such that f(x_1)>f(x_2)a n dg(x_1) f(g(3alpha-4))

consider the functions f(x) = sqrt(x-2) , g(x) = ( x+1)/( x^2 -2x +1) (fg)(x)

Let f:R→R:f(x)=x^2 and g: R→R: g(x)=(x+1) . Show that (gof)≠(fog) .