Question

How do you find the compositions given `f(x) = |x - 2`|, `g(x) = sqrtx`?

Answer 1

`f(g(x))=f(sqrt(x))=|sqrt(x)-2|` and `g(f(x))=g(|x-2|)=sqrt(|x-2|)`

Explanation:

Every function has an input and an output. Composing two functions means to use the output of the first as the input for the second.

So, `f(x)` takes an input `x` and outputs the absolute value of the input minus two.
`g(x)` takes an input `x` and ouputs the square root of the input.

So, `f(g(x))=f(sqrt(x))=|sqrt(x)-2|` and `g(f(x))=g(|x-2|)=sqrt(|x-2|)`