reading the notation as "g of f" or "g after f"
question: How can you memorize the notation?, context: That is, the value of x is obtained by first applying f to x to obtain y = f(x) and then applying g to y to obtain z = g(y). In the notation 



g
∘
f


{\displaystyle g\circ f}

, the function on the right, f, acts first and the function on the left, g acts second, reversing English reading order.  The notation can be memorized by reading the notation as "g of f" or "g after f". The composition 



g
∘
f


{\displaystyle g\circ f}

 is only defined when the codomain of f is the domain of g. Assuming that, the composition in the opposite order 



f
∘
g


{\displaystyle f\circ g}

 need not be defined. Even if it is, i.e., if the codomain of f is the codomain of g, it is not in general true that
How can you memorize the notation?
 The notation can be memorized by reading the notation as "g of f" or "g after f" .
That is, the value of x is obtained by first applying f to x to obtain y = f(x) and then applying g to y to obtain z = g(y). In the notation 



g
∘
f


{\displaystyle g\circ f}

, the function on the right, f, acts first and the function on the left, g acts second, reversing English reading order.  The notation can be memorized by reading the notation as "g of f" or "g after f". The composition 



g
∘
f


{\displaystyle g\circ f}

 is only defined when the codomain of f is the domain of g. Assuming that, the composition in the opposite order 



f
∘
g


{\displaystyle f\circ g}

 need not be defined. Even if it is, i.e., if the codomain of f is the codomain of g, it is not in general true that
 The notation can be memorized by <hl> reading the notation as "g of f" or "g after f" <hl> .
That is, the value of x is obtained by first applying f to x to obtain y = f(x) and then applying g to y to obtain z = g(y). In the notation g ∘ f {\displaystyle g\circ f} , the function on the right, f, acts first and the function on the left, g acts second, reversing English reading order. The notation can be memorized by <hl> reading the notation as "g of f" or "g after f" <hl>. The composition g ∘ f {\displaystyle g\circ f} is only defined when the codomain of f is the domain of g. Assuming that, the composition in the opposite order f ∘ g {\displaystyle f\circ g} need not be defined. Even if it is, i.e., if the codomain of f is the codomain of g, it is not in general true that
That is, the value of x is obtained by first applying f to x to obtain y = f(x) and then applying g to y to obtain z = g(y). In the notation g ∘ f {\displaystyle g\circ f} , the function on the right, f, acts first and the function on the left, g acts second, reversing English reading order. <hl> The notation can be memorized by reading the notation as "g of f" or "g after f" . <hl> The composition g ∘ f {\displaystyle g\circ f} is only defined when the codomain of f is the domain of g. Assuming that, the composition in the opposite order f ∘ g {\displaystyle f\circ g} need not be defined. Even if it is, i.e., if the codomain of f is the codomain of g, it is not in general true that