Invertible Functions in Math

• 
• How to check that this is left-invertible.
  • $f:\{1,2,3\}\to \{a,b,c,d\}$
  • Now we need $g:\{a,b,c,d\}\to \{1,2,3\}$
  • We need to find $g(f(x))=x,\mathrm{\forall }x\in \{1,2,3\}$
  • Since a function needs to be defined for every single input, we need to map $c\to \text{something}$.
  • So let $c\to \text{anything}\to 2$
    • This means there's $3$ inverse functions, because $c\to \text{only 3 things}$.
  • $g(f(1))=g(b)=1$
  • $g(f(2))=g(1)=2$
  • $g(f(3))=g(d)=3$
  • and $c$ isn't hit, so it doesn't matter.
• Right-invertible
  • We can see that nothing from the left side can map to $c$ and come back.