what is composition in math?

Question

is it when you do:

f(f^-1(1))

or

f(f^-1(x))
i know that both would work but what is know as "composition"??

Answer 1

A composition is when you have two functions and combine them like so:

f(x)->y , g(y)->z

then you can compose f and g:

h(x) = f(g(x))

Ex:

f(x) = x^2
g(x)=2x+3

then h(x) = f(g(x)) = (2x+3)^2

note that f(g(x)) is different from g(f(x))