Answer :
Danika is not correct. She forgot to do g compose f.
How to check inverse?
- To verify that functions are inverses of each other, you must also show that g(f(x)) = x.
- Because g(f(x)) = -x, the functions are not inverses of each other.
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:
f(g(x)) = x
Let's prove that this is not fulfilled for these functions, then:
f(x) = |x|
g(x) = -x
f(g(x)) = |-x|
= |-1| |x|
= |x|
i.e., f(g(x)) = |x| ≠ x
As you can see we did not obtain the function that matches the definition of inverse functions.
Hence, we can't agree with Danika.
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