Transformation technique problem

#1
Consider a random variable X having a Uniform distribution with a=0 and b=1 Let Y=| X| Find
the distribution of Y.using transformation technique

This question comes out of math Stat 5th ed. Ans g(y)=0.5. 0<y<1 g(y)=0.4. 3<y<4
g(y)=U(y,0,1)+U(-y,0,1)=2U(0,1)|w’(y)|=1
U(y,0,1)=1
w’(y)=f(y)+f(-y)