निम्नलिखित फलन f और g के लिए `f+g` का मान ज्ञात कीजिए -
`f(x)=x^(4),AAx inR` और `g(x)=x-1,AAx inR`.

If f(x)=x|x|,AAx inR . then :

The function f(x)=e^(x),x""inR is

Let A = {-1,0,1,2}, B = {-4,-2,0,2} and f , g : A rarr B be functions defined f(x) = x^(2)-x, x inR and g(x) = 2 |x-(1)/2|-1,x inR . Are f and g equal ? Justify your answer. (Hint : One may note that two functions f : A rarr B and g : A rarr B such that f (a) = g(a) A a inA, are called equal functions).

Show that f(x)=a^(x),agt0 is increasing for AAx inR .

Prove that f(x)="sin"x-x is decreasing AAx inR .

Prove that cot^(-1)(-x)=pi-cot^(-1)x,AAx inR .

If f (x) = sin x, g(x) = x^(2) , if x inR , then find [(fog)(x)].

If f(x)=(x)/(1+|x|)" for "x inR , then f'(0) =

If f(x)=(x)/(1+|x|)" for "x inR , then f'(0) =

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=