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:
[tex]f(g(x))=x[/tex]
Everything is ok up to this point, right?. But let's prove that this is not fulfilled for these functions, then:
[tex]f(x)=\left | x \right | \\ \\ g(x)=-x \\ \\ f(g(x))=\left| -x \right |=\left | -1 \right | \left | x \right |=\left | x \right | \\ \\ \therefore f(g(x))=\left | x \right | \neq x[/tex]
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.
