`f(x) =3x +(1)/(3x)`

If f(x)= x^(3) + (1)/(x^(3) )(x ne 0) , then its greatest value is-

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

If f(x) = x^(3) - (1)/(x^(3)) then f (x) + f ((1)/(x)) is equal to

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

Find the intervals in which the function f given by f(x) = x^3 + (1/x^3), x ne 0 is increasing.

Find the intervals in which the function f given by f(x) = x^3 + (1/x^3), x ne 0 is decreasing.

If f(x)= x^(3)- (1)/(x^(3)) then show that f(x)+ f((1)/(x))= 0

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

If f(x) = log ((1+x)/(1-x)) , where -1 lt x lt 1 then f((3x+x^(3))/(1+3x^(2))) - f((2x)/(1+x^(2))) is equal to