College Algebra Problems With Answers sample 2 : Composite and Inverse Functions
College algebra problems and questions on composite and inverse functions are presented along with their solutions located at the bottom of the page.
Let f(x) = √(x - 4) + 3.
a) Find the
inverse of f.
b) Find the range of f -1.
Let h(x) = (x - 1) / (-x + 3).
a) Find the inverse of h.
b) Find the range of h.
Let f(x) = (x - 1)/(x + 5) and g(x) = 1/(x + 3).
a) Find the
composite function (f o g)(x).
b) Find the domain of f o g.
Function f is a function with inverse f -1. Function h is defined by h(x) = f(x) + k where k is a constant. Express the inverse function of h in terms of f -1 and k.
Function f is a function with inverse f -1. Function h is defined by h(x) = A*f(x - h) + k where A, k and h are constants. Express the inverse function of h in terms of f -1, A, k and h.
The graphs of functions f and g are shown below.
a) Use the graph to find (f o g)(-4)
b) Use the graph to find (g o f)(1)
Figure 1. Graph of Function f
.
Figure 2. Graph of Function g
Functions f and h are defined by the tables
x
-3
-2
-1
0
1
2
3
f(x)
-6
-4
-2
1
2
6
16
x
0
1
2
3
4
5
6
h(x)
1
2
5
10
17
26
37
Use the values in the tables to find
a) (f o h)(1)
b) (f o f)(0)
c) (f o h)(5)
d) (f o h-1)(5)
e) (h o f-1)(6)
Answers to the Above Questions
f -1(x) = (x - 3)3 + 4 , x≥3
[4 , +infinity) : it is the domain of f
h -1(x) = (-3x - 1) / (x + 1)
(-infinity , -1) U (-1 , +infinity) : it is the domain of h-1
(f o g)(x) = -(x + 2) / (5x + 16)
domain of the composite function f o g : (-infinity , -16/5) U (-16/5 , -3) U (-3 , +infinity)
.