Question

I'm super confused on parts g and h because no formula is given, just the limit values. These are the values:

lim f(x) = 16
x is approaching 4

lim g(x) = -2
x is approaching 4​

Answer 1

See below.

Explanation:

1)

So we have the limit:

`\lim_(x\to 4) (f\circ g)(x)`

This is equivalent to:

`\lim_(x\to 4) f(g(x))`

To solve, we can use the following property:

`\lim_(x \to c) f(g(x))=f( \lim_(x \to c) g(x))`

Therefore, our limit is the same as:

`\lim_(x\to 4) f(g(x))\\=f(\lim_(x\to 4) g(x))`

We are already given that the limit as x approaches 4 of g(x) is -2. Therefore:

`=f(-2)`

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:

`\lim_(x\to 4) (g\circ f)(x)\\=\lim_(x\to 4)g(f(x))`

Using the same property:

`=g(\lim_(x\to 4) f(x))`

And we are told that this is 16, so:

`=g(16)`

And we just need to evaluate this to find the limit.

I hope you find this helpful!