If `f(x)=x^2-1/x^2` then prove that `f(x)+f(1/x)=0`

If f (x) =(x-1)/(x+1), then prove that f{f(x)}=-1/x.

If f(x)=(x^(2)-1)/(x^(2)+1) prove that f((1)/(x))=-f(x)

(i) If f(x) = x + (1)/(x) prove that: [f(x)]^(3) = f(x^(3)) + 3f ((1)/(x)) (ii) If f(x) = x^(3) - (1)/(x^(3)) , prove that f(x) + f((1)/(x)) = 0 (iii) If f(x) = (1-x^(2))/(1+ x^(2)) , prove that f (tan theta) = cos 2 theta

If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^(2))]=2f(x)

If f(x)=x+(1)/(x) , then prove that : {f(x)}^(3)=f(x^(3))+3*f((1)/(x))

If f(x)="log"(1+x)/(1-x) , then prove that: f((2x)/(1+x^(2)))=2f(x)

If f(x)=(x^(2))/(1+x^(2)), prove that lim_(x rarr oo)f(x)=1

f(x)=(ax^(2)+1)/(x^(2)+1),lim_(x rarr0)f(x)=1 and lim_(x rarr oo)f(x)=1, then prove that f(-2)=f(2)=1

Find the derivative of f(x)=2x^2+3x-5 at x=-1. Also, prove that f'(0)+3f'(-1)=0.

If f: R to [0,∞) be a function such that f(x -1) + f(x + 1) = sqrt3(f(x)) then prove that f(x + 12) = f(x) .