Danika concludes that the following functions are inverses of each other because f(g(x)) = x. do you agree with danika? explain your reasoning.
f(x) = |x|
g(x) = –x

We cannot agree with Danika. Why? Well, The reasoning is given as follows:

Two functions are inverses of each other if and only if it is true that the composition function is given by:



Everything is ok up to this point, right?. But let's prove that this is not fulfilled for these functions, then:



As you can see we did not obtain the function that matches the definition of inverse functions. For that reason we can't agree with Danika.