Answer
See below.
Work Step by Step
If $g$ is one-to-one then for all $y=g(x)$ there is only one $x$.
a) $y=7$ for $x=1$ and $x=-1$ thus it is not one-to-one
b) $y=\sqrt{x+3}-5$ is strictly increasing on its domain, thus it is one-to-one
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