1.If `f(x)=x+(1)/(x)` then prove that `|f(x)|^(2)=f(x^(2))+f(1)`

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

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

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

If f(x),=x+(1)/(x), prove that [f(x)]^(3),=f(x^(3))+3f((1)/(x))dots

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

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)