Let X have density function fx(x)=1/x^2 for x>1, otherwise fx(x)=0.

Let Y=X^(1/3). Compute the density function fy(y) for Y.

my attempt

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P(X<=1)=0

P(Y^3<=1)=P(Y<=1)=0

P(1<x<inf)=P(1<Y^3<inf)

=1-P(Y<1)

i am stuck here.

The answer to this is

fy(y) = 3y^4 for y>1 and 0 for y<= 1