If X is continous with distribution function F(x) and pdf f(x). It is given

Y=2X, finding the distribution of Y will be:

Fy(a)= P(Y< a)

= P(2X< a)

= P(X< a/2)

= Fx(a/2)

Differentiation will give me:

fy(a) = 1/2fx(a/2)

What if the relationship is Y= 2 F(X), where F(X) is the cumulative distribution of X. I can't seem to make X the subject of the above equation.