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OWF from PRG and OWF

cn flag

Let $f : \mathcal{U}_{2\lambda} \to \mathcal{U}_{2\lambda}$ be a OWF, and $G : \mathcal{U}_{\lambda} \to \mathcal{U}_{2\lambda}$ be a PRG with $\lambda$-bit stretch. Establish whether the following function $f' : \mathcal{U}_{\lambda} \to \mathcal{U}_{2\lambda}$ is one-way or not: \begin{equation*} f'(x) = f(G(x) \oplus (0^\lambda \| x)) \end{equation*}

I don't know how to solve this. Is this a OWF or not? I think that if $f$ is a OWF also $f'$ is.

cn flag
Hint: a OWF can behave arbitrarily badly on a negligible fraction of its input space and a PRG can directly use part of its seed as a part of its output.
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