(Abstract Algebra 1) Composition of Functions 

Your videos are awesome with great clarity and understanding.

In the last example, g is a function (it passes the vertical line test), but it is not injective (it does not pass the horizontal line test) and it is not surjective (there is no x value that maps to a y value of -5, for example). You can still compute the composition of g and f, however.

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In the last example, does it matter that g:R-->R isn't a function since the images are only R >= -2?