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finding a one to one function

finding a one to one function

magpiemagpie46

Hi all, the following question is for :
Consider the function g: D ® R for which the rule is g(x) = 2 / (2x - 3)^2 + 4, the + 4 is on the numerator and D is themaximal domain of g.
Question:
Find the smallest value of a such that f: (a, ¥) ® R,f(x)= g(x) is a one-to-one function.
Solution: The book gives: 3/2 but i'm not sure where to start with this
I know that a one to one function must satisfy the vertical and horizontal test
Any help would be greatly fantastic

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