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

If f(x)=(1-x)/(1+x), prove that f{f((1)/(x))}=1/x[x ne0]

If f(x)=(1-x)/(1+x) , then prove that f(x)+f(1/x)=0 .

If f(x)=(1-x)/(1+x), prove that f[f{f(1/x)}]=-f(x)

If f(x) = (x-1)/(x+1) , then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/(1+xy) .

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

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

For a function f(x),f(0)=0 and f'(x)=(1)/(1+x^(2)), prove that f(x)+f(y)=f((x+y)/(1-xy))

If f is a real function defined by f(x)=(x-1)/(x+1) , then prove that f(2x)=(3f(x)+1)/(f(x)+3)