Combining functions

Basic concepts

• Numbers as processes and objects:
  "$x+y$" is the number you get by counting to $x$, and then continuing to count, while simultaneously counting $y$
• Functions as processes and objects. In what follows, suppose that $f$ and $g$ are functions:
  • $f^{-1}$ is the function defined by $f^{-1}(y)=x$, if and only if $y=f(x).$
  • $g\circ f$ is the function defined by $(g\circ f)(x)=g(f(x))$.
  • $f+g$ is the function defined by $(f+g)(x)=f(x)+g(x)$.
  • $f-g$ is the function defined by $(f-g)(x)=f(x)-g(x)$.
  • $fg$ is the function defined by $(fg)(x)=f(x)g(x)$.
  • $f/g$ is the function defined by $(f/g)(x)=f(x) / g(x)$.

[10.3] Combination examples

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