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Pope asked in Science & MathematicsMathematics · 5 months ago

Domain of composite function?

Let functions f and g be defined by their graphs, a ray in both cases.

h(x) = f[g(x)]

What is the domain of the composite function h?


This was not actually my question. Someone else asked it early this year. I was trying to understand the disappointing responses. Two people (now three) argued that the domain of h was the intersection of domains of f and g. One other person said that the composite function was not possible.

For starters, there is no g(-3), so of course there can be no f[g(-3)].

I will keep checking for a while. It is not a trick question. Surely someone will get it.

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1 Answer

  • 5 months ago

    If the function composition, f(g(x)), exists, then the domain of f(g(x)) is ALWAYS the domain of g.  For the function composition to exist the range of g must be a subset of the domain of f.  

    From your graph, the range of g is [1, -∞) and the domain of f is [-3, ∞).

    [1, -∞) is not a subset of [-3, ∞) so the function composition doesn't exist.

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