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)=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)=(1)/(1+x^(2)) and g(x) is the inverse of f(x) ,then find g(x)

Let f and g be two functions defined by f(x)=(x)/(x+1), g(x) =(x)/(1-x) . If ( f o g ) ^(-1) (x) is equal to kx, then find the value of k.

Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), then g'(3) equals _

f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x)-g''(x)=0, f'(1)=2, g'(1)=4, f(2)=3 and g(2)=9 , then [f(x)-g(x)] at x=(3)/(2) is equal to -

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^2 and g(x)=sinx for all xIR then the set of all x satisfying (f o g o g o f ), (x)=(g o g o f) , (x) , where (f o g ) , (x)=f(g(x)) , is

Let f(x)a n dg(x) be two continuous functions defined from RvecR , such that f(x_1) > f(x_2) and g(x_1) x_2 dot Then what is the solution set of f(g(alpha^2-2alpha) > f(g(3alpha-4))

Let f:RR rarr RR and g: RR rarr RR be two functions such that (g o f) (x) = sin ^(2) x and ( f o g) (x) = sin (x^(2)) . Find f(x) and g(x) .

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2