`-23.F a c t o r i z e :(x^2+1/(x^2))-4(x+1/x)+6`

Let f : R to R : f (x) = (2x -3) " and " g : R to R : g (x) =(1)/(2) (x+3) show that (f o g) = I_(R) = (g o f)

Let f: R->R \ w h e r e \ f(x)=(x^2+4x+7)/(x^2+x+1) . Is f(x) \ on e \ on e ?

Let f: R->R \ w h e r e \ f(x)=(x^2+4x+7)/(x^2+x+1) . Is f(x) \ on e \ on e ?

Observer the following statements : A : int (x^(2)-1)/(x^(2)) e^((x^(2)+1)/(x))dx=e^((x^(2)+1)/(x))+c R: int f'(x)e^(f(x))dx=f(x)+c Then which of the following is true ?

Observe the following statements A : int (((x^(2)-1)/(x^(2))).e^((x^(2)+1/x)) dx = e^((x^(2)+1)/x) + c R: int f^(')(x).e^(f(x)) dx = f(x) + c Then which of the following is true?

Column I, Column II y=(x^2-2x+4)/(x^2+2x+4),x in R ,t h e ny c a nb e , p. 1 y=(x^2-3x-2)/(2x-3),x in R ,t h e ny c a nb e , q. 4 y=(2x^2-2x+4)/(x^2-4x+3),x in R ,t h e ny c a nb e , r. -3 x^2-(a-3)x+2<0,AA,x in (-2,3),t h a nac a nb e , s. -10

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+1)) .