### Home > A2C > Chapter 6 > Lesson 6.2.5 > Problem 6-118

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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!