# Limits of composition functions?

Given the graphs below, how can you find the following:

5. 𝑙𝑖𝑚𝑥→6− 𝑔(1 − 𝑓(𝑥))

6. 𝑙𝑖𝑚 𝑥→3+ 𝑓(15 − (𝑥 ^2))

### 1 Answer

Relevance

- AlanLv 74 months ago
5.

first (1- f(x)) as x -> 6- (from the left)

f(x) =1 as x->6-

1- 1 = 0

g(0) is the answer to this question

g(0)= -2

so answer to 5.

is = -2

6,

f(15 -x^2) as x->3+

x^2 from the right at x =3

x^2 approaches 9 from the right

so as it approaches 9 , it is greater than 9

15 -x^2 approaches 6 from the left

15 -x^2 is approaches 6 from the left

f(x) as you approach 6 from the left is 1

so the answer is 1

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