SOLUTION: Let f:R to R and g:R to R and f(x) is defined by f(x)=2-3x and g (x) is a quadratic function.If (fog)(x)=3x^2-9x-4 find g (x) I got my answer x^2-2x-2=0 Is it correct ? Could

Algebra ->  Functions -> SOLUTION: Let f:R to R and g:R to R and f(x) is defined by f(x)=2-3x and g (x) is a quadratic function.If (fog)(x)=3x^2-9x-4 find g (x) I got my answer x^2-2x-2=0 Is it correct ? Could      Log On


   

Question 1069269: Let f:R to R and g:R to R and f(x) is defined by f(x)=2-3x and g (x) is a quadratic function.If (fog)(x)=3x^2-9x-4 find g (x)
I got my answer x^2-2x-2=0
Is it correct ?
Could you give a full solution

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(fog)(x) means apply g(x) first then f(x)
:
f(x) = 2 - 3x
:
g(x) = Ax^2 + Bx + C
:
(fog)(x) = 2 - 3(Ax^2 + Bx + C)
:
2 - 3Ax^2 - 3Bx - 3C = 3x^2 - 9x - 4
:
-3Ax^2 -3Bx - 3C = 3x^2 -9x - 6
:
Ax^2 + Bx + C = -x^2 +3x + 2
:
******************
g(x) = -x^2 +3x +2
******************
:
to check the answer calculate (fog)(x)
:
2 - 3(-x^2 +3x +2) =
:
2 + 3x^2 -9x -6 =
:
3x^2 - 9x -4
:
our answer for g(x) checks
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