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

If f(x)=x+1/x show that (f(x))^3=f(x^3)+3 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

ff(x)=x+(1)/(x), thenprovethat [f(x)]^(3)=f(x^(3))+3f((1)/(x))

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

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)}^(3)=f(x^(3))+3*f((1)/(x))

If y=f(x)=(3x+1)/(5x-3) , prove that x=f(y).

If f(x)=3^(x) , then prove that f(x + 1) = 9f(x - 1).

If y= f(x) =(3x-1)/(5x-3) , prove that f(y) =x.

If f(x)=x+(1)/(x) , such that [f(x)]^(3)=f(x)^(3)+lambdaf((1)/(x)) , then lambda=