Answer
(a) not one-to-one.
(b) one-to-one.
Work Step by Step
(a) $y=4x^2+3 \Longrightarrow x=\pm\frac{1}{2}\sqrt {y-3}$, for some y-values, there are more than 1 x-values, thus it is not one-to-one.
(b) $y=\sqrt {x+3}-5 \Longrightarrow x=(y+5)^2-3$, for each y-value, there is only one x-value, thus it is one-to-one.
