Obviously I'm stuck. The question is to find the density function, Y = 2X.

Fy(a) = Pr{Y<=a}

= Pr{2X<=a}

= Pr{X<=a/2}

= Fx(a/2)

Differentiate both Fy and Fx cdfs

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

I don't understand where the 1/2 comes from. Differentiating a cdf like F(a) results in the density function f(a), so wouldn't differentiating Fx(a/2) produce fx(a/2)?