Limits of composition functions?

Question

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))

Answer 1

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