Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
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.
1 Answer
- Demiurge42Lv 78 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.
