Questions, with their detailed solutions, on the compositions of functions are presented.

Some of the questions are about finding the composition of two functions and its domain. An answer to one of these questions is correct when both the formula of the function and the domain are correct. Also examples of Applications of Composition of Functions are included in this site.

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5 questions are presented in this page and more may be accessed using the applet below.

Question 1: Find the composition function (f _{o} g) (x) and its domain.

f(x) = x + 1 , g(x) = 3x

Question 2: Find the composition function (f _{o} g) (x) and its domain.

f(x) = x^{ 2} + 1 , g(x) = sqrt(2 x)

Question 3: Find the composition function (f _{o} g) (x) and its domain.

f(x) = sqrt(-x + 1) , g(x) = x^{ 2} - 8

Question 4: Find, if possible, (f _{o} g) (-2).

f(x) = 2x + 1 , g(x) = x^{ 2}

Question 5: Find, if possible, (f _{o} g) (0).

f(x) = 1 / (x + 1) , g(x) = 1 / (x - 1)

More Question on Composition of Functions - Using an applet

"inf" is used to mean infinity. A total of 10 questions with their answers are included in the test.

click on the button above "click here to start" and MAXIMIZE the window obtained.

click start on the main menu.

answer the question by checking a,b,c,d or e in the lower part of the
window.

You can review your answers and change them by checking the desired letter.
Once you have finished, press "finish" and you get a table with your answers and the right answers to compare with.