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)

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)