`f f(x)=x+1/x ,t h e n p r o v e t h a t[f(x)]^3=f(x^3)+3f(1/x)`

Evaluate: int(x)i spol y nom i a lfu n c t ionoft h en t h degr e e ,p rov et h a t- inte^xf(x)dx=e^x[f(x)f^(prime)(x)+f^(x)=f^(x)++(-1)^nf^((n))(x)] Where f^((n))(x)d e not e s(d^nf)/(dx^n)

Let f: R to R be a periodic function such that f(T+x)=1" " where T is a +[1-3f(x)+3(f(x))^(2) -(f(x))^(3)]^(1/3) fixed positive number, then period of f(x) is

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=x^3-x^2+100x+2002 ,t h e n a) f(1000)>f(1001) b) f(1/(2000))>f(1/(2001)) c) f(x-1)>f(x-2) d) f(2x-3)>f(2x)

Let f be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then prove that f(x)=(x^(3))/(3)+x^(2)

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1/(2001)) f(x-1)>f(x-2) f(2x-3)>f(2x)

If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1/(2001)) f(x-1)>f(x-2) f(2x-3)>f(2x)