6: Function Algebra

”As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.” - Joseph-Louis Lagrange

Chapter six takes a step back to look at how new functions are formed out of old ones. We look at how addition, subtraction, multiplication, and division have inspired almost all of the functions we have seen thus far, and how they impact their domains as well.

We turn our attention to a fifth operation between two functions: composition. This naturally leads to a discussion about one-to-one and inverse functions. The reader is given the tools to confirm two functions are inverses, and discover the inverse of a given function.

The easiest application of the inverse is the radical function, which is already in our vocabulary. We discuss some basic properties of this family of inverse functions and demonstrate taking limits involving radicals, and how to use the difference of power formula to help factor and reduce expressions.

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