1. ## Composition,Domain,Notation?

(a)
Let f(x) = |x - 2|, g(x) = √x (square root of x) and h(x) = x^-1 (x to the power of -1).
Find the following COMPOSITIONS and state their DOMAIN in INTERVAL NOTATION:
(i) f ○ g
(ii) h ○ g
(iii) (h ○ g) ○ f

(b)
Let f(x) = 1 ÷ sin(x + π).
Express f(x) as a COMPOSITIONS of three functions (in the right order!) and state the DOMAIN of f in SET NOTATION.

The question asks part (a) compostion & domain in interval notation.
Part (b) asks composition & domain in set notation.

{ } ∩ U ] [ ( ) | ≤ ≥ ∞ Є ÷ ○ π

2. Originally Posted by federer
(a)
Let f(x) = |x - 2|, g(x) = √x (square root of x) and h(x) = x^-1 (x to the power of -1).
Find the following COMPOSITIONS and state their DOMAIN in INTERVAL NOTATION:
(i) f ○ g
(ii) h ○ g
(iii) (h ○ g) ○ f

(b)
Let f(x) = 1 ÷ sin(x + π).
Express f(x) as a COMPOSITIONS of three functions (in the right order!) and state the DOMAIN of f in SET NOTATION.

The question asks part (a) compostion & domain in interval notation.
Part (b) asks composition & domain in set notation.

{ } ∩ U ] [ ( ) | ≤ ≥ ∞ Є ÷ ○ π
$f(x) = |x-2|$
$g(x) = \sqrt{x}$

$f[g(x)] = |\sqrt{x}-2|$

It's domain is all non-negative numbers because you cannot take the square root of a negative number.