Composition of Functions Questions

Questions on the compositions of functions along with their detailed solutions are presented. There is also a tutorial on compositions of functions that may be used.
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.

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) = √(2 x)

Question 3

Find the composition function (f o g) (x) and its domain.
f(x) = √(-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)

detailed solutions to the above questions.

More References and links

Maths Problems, Questions and Online Self Tests
Questions on Composite Functions with Solutions.