identify if the functions are pseudorandom generator?
$G'$ is a PRG. Proof sketch: by assumption, $G(x)$ for a uniform $x$ is indistinguishable from a uniform string. This means that $y_1$ and $y_2$ (the halves of $G(x)$) are also indistinguishable from uniform strings, and finally that so are $G(y_1)$ and $G(y_2)$.