Question

What is function composition?

Answer 1

See the explanation.

Explanation:

Informal speaking: "it's a function of function".
When you use one function as a argument of the other function, we speak of the composition of functions.

`f(x) diamond g(x) =f(g(x))` where `diamond` is composition sign.

Example:

Let `f(x)=2x-3, g(x)=-x+5`. Then:

`f(g(x))=f(-x+5)`

If we substitute:

`-x+5=t => x=5-t`

`fdiamondg=f(t)=2(5-t)+3=10-2t+3=13-2t`
`fdiamondg=13-2x`

You can, however, find `g(f(x))`

`g(f(x))=g(2x-3)`

`2x-3=t => x=(t+3)/2`

`gdiamondf=g(t)=-((t+3)/2)+5=-t/2+7/2`

`gdiamondf=-x/2+7/2`

Answer 2

Refer to explanation

Explanation:

Combining two functions by substituting one function's formula in place of each `x` in the other function's formula.
The composition of functions `f` and `g` is written `fog`, and is read "f composed with g." The formula for `fog` is written `(fog)(x)`.
The domain and range for the functions are `f:A->B` and `g:B->C`