I know that order of composition matters between two functions. But is there a case where you can not compose a function with another?
Is it always possible to compose one function with another?
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algebra-precalculus
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0Yes. For example $f(x)= \sqrt{x}$ and $g(x)=-x^2-\sqrt{-x-1}$ cannot be composed. – 2017-02-02
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3More generally, the composition $f(g(x))$ doesn't make any sense if the intersection of the range of $g(x)$ and the domain of $f(x)$ are the empty set. – 2017-02-02
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0More properly most authors require for the [function composition](https://en.wikipedia.org/wiki/Function_composition) $f\circ g$ that the range of $g$ be contained in the domain of $f$. – 2017-02-02
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2You can always compose two functions. Sometimes this composition may be undefined everywhere. So, it depends what you're looking for in a composition. – 2017-02-02