Answer:
See below.
Step-by-step explanation:
1)
So we have the limit:
[tex]\lim_{x\to 4} (f\circ g)(x)[/tex]
This is equivalent to:
[tex]\lim_{x\to 4} f(g(x))[/tex]
To solve, we can use the following property:
[tex]\lim_{x \to c} f(g(x))=f( \lim_{x \to c} g(x))[/tex]
Therefore, our limit is the same as:
[tex]\lim_{x\to 4} f(g(x))\\=f(\lim_{x\to 4} g(x))[/tex]
We are already given that the limit as x approaches 4 of g(x) is -2. Therefore:
[tex]=f(-2)[/tex]
You simply need to evaluate this to solve the limit. I don't have enough information to solve this, so maybe you have something more.
Similarly, for the second one:
2)
We have:
[tex]\lim_{x\to 4} (g\circ f)(x)\\=\lim_{x\to 4}g(f(x))[/tex]
Using the same property:
[tex]=g(\lim_{x\to 4} f(x))[/tex]
And we are told that this is 16, so:
[tex]=g(16)[/tex]
And we just need to evaluate this to find the limit.
I hope you find this helpful!
