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Let f(x)=x^2-7x+18 and let g(f(x))=2x+3. What is the sum of all possible values of g(8)?

Guest Feb 7, 2018
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We are looking for the values that make  f(x)  =   8

 

So we have

 

x^2 - 7x + 18  =  8       subtract 8 from both sides

 

x^2 - 7x  +  10  =  0      factor

 

(x - 5) ( x - 2)  = 0

 

Setting each factor to 0 and solving for x we have that  

 

x  = 5  or   x  =  2

 

So.....g(8)  =  either     2(5) + 3   =  13    or

 

                                    2(2)  + 3   =  7

 

And the sum of these  =   20

 

 

cool cool cool

CPhill  Feb 7, 2018

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