College Algebra & Trigonometry, 2018a

4.7. COMPOSITE FUNCTIONS 227
Exercises 4.7
Find f ◦ g(x) and g ◦ f(x) for each of the following problems.
1) f(x) =x 2 2) f(x) =|x − 3|
g(x) =x − 1 g(x) =2x +3
3) f(x) = x
x − 2
g(x) = x +3
x
4) f(x) =x 3 − 1
g(x) = 1
x 3 +1
5) f(x) = √ x +1 6) f(x) =2x 3 − 1
g(x) =x 4 − 1 g(x) = 3 √
x +1
2
Find functions f(x) and g(x) so that the given function h(x) =f ◦ g(x)
7) h(x) =(3x +1) 2 8) h(x) =(x 2 − 2x) 3
9) h(x) = √ 1 − 4x 10) h(x) = 3√ x 2 − 1
11) h(x) =
( ) 2 x +1
12) h(x) =
x − 1
( ) 3 1 − 2x
1+2x
13) h(x) =(3x 2 − 1) −3 14) h(x) = ( 1+ 1 x
) −2
√ x
15) h(x) =
x − 1
16) h(x) = 3 √
x − 1
x