What is the composition of $f$ and $g$ if $$ f: \{a, b, c\} → \{a, b, c\}$$ and $$ g: \{a, b, c\}→\{1, 2, 3\}$$ $f(a)=a, f(b)=b, f(c)= c$ and $g(a)=1, g(b)=2, g(c)=3$
What I think:
I don't think it's possible for the function g to be nested inside of the function $f$ since the codomain of $ g $ would always be $1, 2$ or $3$ but function f's domain would be $ a, b, $ or $ c$ which isn't $1, 2$ or $ 3. $ Would this be a correct assumption?
Hint: Composition is defined with $$(g\circ f) (x) = g(f(x))$$
so $$(g\circ f) (a) = g(f(a)) = g(a) = 1$$
Notice that $f\circ g$ does not exist.