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For part c) what is the point of the "g(x)=f(x)"? It didn't seem to effect the final answer (-infinite, 0] but what was its purpose, if it had one?

Thanks

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    I suppose your alternatively would be to just say that $f$ in invertible in $(-\infty, 0]$. The thing is $f$'s domain has already been defined as $\mathbb R$. If you change its domain, it's no longer $f$, it's something different. The question begins by giving this "different thing" in the name of $g$. – 2017-02-18

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