COMPOSITE FUNCTIONS ASSIGNMENT

Functions f and g are give by
f(x) = √(x + 2) and g(x) = ln (1 – x ²)
Find the composite function defined by (g _o f)(x) and describe its domain.

Functions f and g are as sets of ordered pairs
f = {(-2,1),(0,3),(4,5)}
and
g = {(1,1),(3,3),(7,9)}
Find the composite function defined by g _o f and describe its domain and range.

Write function F given below as the composition of two functions f and g
F(x) = | 4 x ² + 2x – 5 |

Write function F given below as the composition of two functions f and g, where g(x) = 1 / x and F(x) = (1 / x) / (1 + x).

g(x) is a piecewise function defined by:
f(x) = x for x < 0
and
f(x) = x ² for x ≥ 0.
Function g is defined by g(x) = √x. Find the composite function g(f(x)).

1. Evaluate f(g(3)) given that
   f(x) = | x – 6 | + x ² – 1 and g(x) = 2x
2. Find f(x) and g(x) if the composite function
   f(g(x)) = 2 sec(2x + 1)
3. Find the domain of the composite function
   g _o f if f(x) = √x and g(x) = 1 / x.

1. Find the range of the composite function f(g(x)) given that
   f(x) = x + 4 and g(x) = x ² + 2
2. Find the composite function (f o g)(x) given that
   f = {(3,6) , (5,7) , (9,0)} and g = {(2,3) , (4,5) , (6,7)}
3. Find the composite function (f o g)(x) given that
   f = {(1,6) , (4,7) , (5,0)} and g = {(6,1) , (7,4) , (0,5)}