1. ## Composite functions question

State the domain of f ° g(x) and g ° f(x) if f(x) = √x and g(x) = 2x - 4

I'm just starting to work with composite functions, I have the solution to this question, but I cannot grasp how it works, can someone please give me some pointers? Here's the answer:

f ° g(x) = f(g(x))
=f(2x-4)
=
√(2x-4)***
f ° g(x) is defined as long as 2x - 4 0 ; 2x 4 ; x 4/2 ; x 2
the domain of f ° g(x) is {x | x 2, x R}

g ° f(x) = g(f(x))
=g(√x)
=2(√x) - 4***
g ° f(x) is defined as long as x 0
the domain of g° f(x) is {x | x ≥ 0, x R}

***These marked parts are where I am becoming confused, I can't figure out what is being done to 2x-4 to make
√(2x-4), or what is being done to √x to make 2(√x) - 4.

2. ## Re: Composite functions question

Originally Posted by Lethargic
State the domain of f ° g(x) and g ° f(x) if f(x) = √x and g(x) = 2x - 4

Assuming that the functions are mapping on the same set then:
$\displaystyle \text{Dom}(f\circ g)=\text{Dom}(f)\cap\text{Dom}( g)$