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)

    college algebra problem 4, function f(x) .

    college algebra problem 4, function g(x) .


  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: 2 April 2013

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