Does anyone understand how to find domain and range of a composite function based on a graph?

Question

anonymous · Answer

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anonymous · Answer

My teacher show me this method (2nd image) i dont quite understand. Does anyone understand it? also, is the picture showing f(g(x)) or g(f(x)) it might be wrong.

anonymous · Answer

so for f(g(x)) the domain of f(g(x)) is the range of g that overlaps the domain of f.  the range of f(g(x)) is the output of that domain.

so the range of g that overlaps with the domain of f is x: [0, 3]
the ouput of f for that input is y: [0, 2]

anonymous · Answer

does that make sense?

anonymous · Answer

is the 2nd image showing a f(g(x)) or g(f(x))?

anonymous · Answer

which goes first when we are solving f(g(x))?

anonymous · Answer

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