Question

2. Given the expression f(g(k(x))), where f, g, and k are functions, what operation should be

performed first? Does the order matter? Why or why not?

Answer 1

See explanation

Explanation:

The expression
`f(g(k(x)))` is the composition of three functions.

The function composition is an operation that takes two functions f and g and produces a function h such that
`h(x) = g(f(x))`

Here the function f(x) is the input. The order in function composition matters! You always compose functions from right to left.

So, in your case, the first input is k(x), then the second input is g(k(x)), and only then you'll find f(g(k(x))).

Example:

`f(x)=2x+1\\ \\g(x)=x^2\\ \\k(x)=x-1`

then

`f(g(k(x)))=f(g(x-1))=f((x-1)^2)=2(x-1)^2+1=2x^2-4x+3`

If you change the order of operations, you'll get another result, for example

`f(k(g(x)))=f(k(x^2))=f(x^2-1)=2(x^2-1)+1=2x^2-1`