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Sequences of Transformations and Finding Domains

I need a sequence of transformations that will transform the graph of 'f' into the graph of 'g' where f(x)=x[squared]+1 and g(x)=(x+3)[squared]-4.

m(x)= [the sqare root of] (4x+12) [divided by] (2x[squared]-7x+5).
(I need to find the domain of m, using interval notation).

Solution Summary

Sequences of transformations and domains are investigated. The solution is detailed and well presented.