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)?
+128407 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
