Image measure of Lebesgue measure under $u(x)=|x|$

Question

Let $\lambda$ be the Lebesgue measure on $\mathbb{R}$ and let $u: \mathbb{R}\rightarrow\mathbb{R}$ be given by $u(x)=|x|$. Observe the image measure $\mu=\lambda \circ u^{-1}$ and determine $\mu([0,a]), \mu([-a,a]),\mu([a,a+1])$.

My suggestions are as follows:

1. $\lambda \circ u^{-1}([0,a])=\lambda([-a,a])=2a$.

2. $\lambda \circ u^{-1}([-a,a])=\lambda([-a,a])=2a$.

3. $\lambda \circ u^{-1}([a,a+1])=\lambda([a,a+1] \cup [-a-1,-a])=2$.

Can anyone confirm if my understanding is correct?

Thank you!