# College Algebra Problems With Answers sample 2 : Composite and Inverse Functions

A set of college algebra problems, with answers, are presented. The solutions are at the bottom of the page.
1. Let f(x) = √(x - 4) + 3.

a) Find the inverse of f.

b) Find the range of f -1.
2. Let h(x) = (x - 1) / (-x + 3).

a) Find the inverse of h.

b) Find the range of h.
3. 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.
4. 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.
5. 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.
6. 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)

.

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7. 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)

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Updated: February 2015