Question

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

Answer 1

For the answer to the question above asking, do you agree with Danika that she concludes that the following functions are inverses of each other because f(g(x)) = x.?

No because,
f(g(x) = |g(x)| = |-x| = |x| ≠ x
g(f(x)) = - |x| ≠ x
I hope my answer helped

Answer 2

We found a counterexample that proves that Danika is incorrect.

Is Danika correct?

Here we have the functions:

f(x) = |x|

g(x) = -x

Danika says that:

f(g(x)) = x

Let's find a counterexample.

If we take x = -1, then:

g(x) = -(-1) = 1

So:

f(g(-1)) = f(1) = |1| = 1

This is different from the value of x, which is -1, so Danika is incorrect.

If you want to learn more about absolute values, you can read:

https://brainly.com/question/1782403