Domains of Compositions

Examples

Range of f is [8,17]; domain of g is [6, 12].
(Domain of g) intersect (Range of f) on the diagonal is AB.
Project AB horizontally to the graph of f.
(x - 2)2 + 8 = 9 implies x = 1.
(x - 2)2 + 8 = 12 implies x = 4.
Then project vertically to the x-axis.
The domain of g(f) is [1,4].

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