SOLUTION: If f(x) = 2x + 4, and g(x) = (x^2 + x +5), find g (f(x)). I have solved to g(f(x)) = ((2x + 4)^2 + (2x + 4) + 5) 4x^2 + 8x + 8x + 16 + 2x + 4 + 5 4x^2 + 18x + 25 Then I a

Algebra ->  Rational-functions -> SOLUTION: If f(x) = 2x + 4, and g(x) = (x^2 + x +5), find g (f(x)). I have solved to g(f(x)) = ((2x + 4)^2 + (2x + 4) + 5) 4x^2 + 8x + 8x + 16 + 2x + 4 + 5 4x^2 + 18x + 25 Then I a      Log On


   

Question 535558: If f(x) = 2x + 4, and g(x) = (x^2 + x +5), find g (f(x)).
I have solved to
g(f(x)) = ((2x + 4)^2 + (2x + 4) + 5)
4x^2 + 8x + 8x + 16 + 2x + 4 + 5
4x^2 + 18x + 25
Then I am stuck. I am wondering if I did some arithmetic error that I am not seeing or if I just cannot find the right factor.
Answer by fcabanski(1391) About Me  (Show Source):
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That's the answer unless you're trying to find the roots.


4x^2 + 18x +25 = 0 Cannot factor, so use the quadratic formula to find the solutions.


a = 4, b=18, c = 25 (-b + or - sqrt (b^2-4ac))/2a =


(-18 + or - sqrt (324-4*4*25))/8 = (-18 + or - sqrt (-76))/8=


(-18 + or - sqrt(-1)*sqrt(4)*sqrt(19))/4 =


(-18 + or - 2isqrt(19))/4 =


(-9/4) + (1/2)i*sqrt(19) or (-9/4) - (1/2)i*sqrt(19)