### Home > CCA2 > Chapter 5 > Lesson 5.2.5 > Problem5-121

5-121.

Consider two functions f(x) = log x and $g ( x ) = | x |$. 5-121 HW eTool (Desmos). Homework Help ✎

1. Use these two functions to write an equation for a composite function and sketch its graph.

2. Use these two functions to write a different composite function and sketch its graph.

3. What makes the two composite functions so different from each other?

4. Challenge: Now try graphing g(f(g(x))).

Use the eTool below to view the graph of the equations and solve the parts of the problem.
Click the link at right for the full version of the eTool: CCA2 5-121 HW eTool

A composition of two functions is when the output of the first function becomes the input of the second.

g(f(x)) = |log(x)| or
f(g(x)) = log|x|

See part (a).

Remember that the order of composition matters.

When using the absolute value first, you can use both positive and negative numbers for x, so the domain is different from the domain for the log function.When using the log first and then taking the absolute value, only positive values can be used for x. If the result of the log is negative, the absolute value makes it positive, so the range is only positive numbers.

Think this through; you can do it!