By definition, a function is even if:
f(x) = f(-x)
For every value of x.
We will find that the correct answer is:
[tex]\lim_{x \to -7}-g(x) = 2\\\\\lim_{x \to -7} g(x) = -2[/tex]
Let's see how we got this:
Now that we know this, knowing that:
g(x) is even
[tex]\lim_{x \to 7}-g(x) = 2[/tex]
From the above limit we can conclude that -g(7) ≈ 2
Then using the even property of g(x) is easy to see that:
[tex]\lim_{x \to -7}-g(x) = 2\\\\\lim_{x \to -7} g(x) = -2[/tex]
Because we also should have -g(-7) = -g(7) ≈ 2
If you want to learn more, you can read:
https://brainly.com/question/16941091
