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))

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1 Answer

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  • Alan
    Lv 7
    4 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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