SOLUTION: (10 pts) Let f (x) = 3x^2 - x - 7 and g(x) = 3x - 1 (a) Determine the composite function (f ∘ g)(x) and simplify the results. Show work. (b) Compute (f ∘ g

Algebra ->  Expressions -> SOLUTION: (10 pts) Let f (x) = 3x^2 - x - 7 and g(x) = 3x - 1 (a) Determine the composite function (f ∘ g)(x) and simplify the results. Show work. (b) Compute (f ∘ g      Log On


   

Question 1135884: (10 pts) Let f (x) = 3x^2 - x - 7 and g(x) = 3x - 1
(a) Determine the composite function (f ∘ g)(x) and simplify the results. Show work.



(b) Compute (f ∘ g)(-1) . Show work.
Answer that was provided on the site is not correct
 
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let f+%28x%29+=+3x%5E2+-+x+-+7+and g%28x%29+=+3x+-+1+
(a) Determine the composite function (f ∘ g)(x) and simplify the results. Show work.
(f ∘ g)(x) =f%28g%28x%29%29
(f ∘ g)(x) =f%283x+-+1%29
(f ∘ g)(x) =3%283x+-+1%29%5E2+-+%283x+-+1%29+-+7
(f ∘ g)(x) =3%289x%5E2+-+6x%2B1%29+-+3x+%2B1+-+7
(f ∘ g)(x) =27x%5E2+-+18x%2B3+-+3x+%2B1+-+7
(f ∘ g)(x) =27x%5E2+-+21x+-+3

(b) Compute (f ∘ g)(-1) .
(f ∘ g)(-1) =27%28-1%29%5E2+-+21%28-1%29+-+3
(f ∘ g)(-1) =27+%2B21+-+3
(f ∘ g)(-1) =45


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(f o g)(x) = 3(3x-1)^2 -(3x-1) -7 = 3(9x^2 -6x +1) -3x +1 -7 =
:
27x^2 -18x +3 -3x +1 -7 = 27x^2 -21x -3
:
(f ∘ g)(x) = 27x^2 -21x -3
:
I assume the problem does not want the inverse of the composite
:
Rather, just evaluate the composite at x = -1
:
(f o g)(-1) = 27(-1)^2 -21(-1) -3 =
:
27 +21 -3 = 45
: