Help finding the limit of a composite function graphically!

Question

blackstreet23 · Answer

attachment

anonymous · Answer

hared to read, but it looks like the limit in g is -2

blackstreet23 · Answer

yes it is, but how do i find the limit of the entire composite function?

perl · Answer

$$ \lim_{x \rightarrow -1} f(g(x)) = f (\lim_{x \rightarrow -1}g(x))$$

blackstreet23 · Answer

Sorry, i do not understand what do you mean by that

blackstreet23 · Answer

do i multiply it?

perl · Answer

you can first find the limit of g(x) as x approaches -1

blackstreet23 · Answer

yes, i did that, but i am stocked at the second step

blackstreet23 · Answer

g(x) = -2, what do i do after i have this piece of information?

perl · Answer

now plug that into f(x) , f(-2) = ?

blackstreet23 · Answer

2?

perl · Answer

yes, looks like 2

blackstreet23 · Answer

does not matter it does not have a close circle on the line in the graph?

perl · Answer

its ok since you are finding the limit of g(x) as x approaches -1.

blackstreet23 · Answer

is it not as x approaches -2?

perl · Answer

the problem was as x approaches -1

blackstreet23 · Answer

ohh yeah but i mean the whole composite function

perl · Answer

let me state the composition of limits rule

blackstreet23 · Answer

because       F(x) = c    right? 
              lim x-->c

perl · Answer

$$\text{If f is continuous at b and }\lim_{x \rightarrow a}g(x)=b \ \ \text{then} \lim_{x \rightarrow a}f(g(x))= f(\lim_{x \rightarrow a}g(x))=f(b)$$

perl · Answer