SOLUTION: If g(f(x)) = 9 - 6x, f(x) = 3x - 2, and g(x) = ax + b, then g(x) = a) 21 - 18x b) 21 - 12x c) 10 - 2x d) 10 - x e) 5 - 2x

Algebra ->  Functions -> SOLUTION: If g(f(x)) = 9 - 6x, f(x) = 3x - 2, and g(x) = ax + b, then g(x) = a) 21 - 18x b) 21 - 12x c) 10 - 2x d) 10 - x e) 5 - 2x       Log On


   

Question 805507: If g(f(x)) = 9 - 6x, f(x) = 3x - 2, and g(x) = ax + b, then g(x) =
a) 21 - 18x
b) 21 - 12x
c) 10 - 2x
d) 10 - x
e) 5 - 2x
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Use the given f and g to form their composition g(f(x)). Note that the definition for g uses variables, "a" and "b".

g%28f%28x%29%29=a%283x-2%29%2Bb
3ax-2a%2Bb

This expression needs to be equal to how the composition was first defined in the given information.
g%28f%28x%29%29=9-6x=3ax-2a%2Bb
9-6x=b-2a%2B3ax
Look at the corresponding parts.
9=b-2a and -6x=3ax
.
The second equation here shows -6=3a, so highlight%28a=-2%29
Allowing you to solve for b, in 9=b-2a, 9=b-2%28-2%29, 9=b%2B4, highlight%28b=5%29

NOW, you finish finding g(x).