SOLUTION: Hi there, I'm having trouble with this problem: Let f(x) = 3x^2 + 7x � 5 and g(x) = 2 � x. (a) Evaluate the function g � f for x = �1. That is, find (g � f)(�1).

Question 1037161: Hi there, I'm having trouble with this problem:
Let f(x) = 3x^2 + 7x � 5 and g(x) = 2 � x.
(a) Evaluate the function g � f for x = �1. That is, find (g � f)(�1).

(2 - x) - (3x^2 + 7x -5)
answer: -3 + 3x^2 + 6x

(b) Evaluate the function fg for x = �1. That is, find (f g)( �1).

(2 - x)(3x^2 + 7x -5)

answer: 2x^2 + 9x - 10

(c) Find the difference function (f � g)(x) and simplify the results.
answer: 3x^2 + 8x - 7

am I doing this correctly? I really appreciate any help!

Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
I think that you are forgetting
to watch your signs.
a)(g-f)(-1)
(2 - x) - (3x^2 + 7x -5)
2 - x - 3x^2 - 7x + 5
Collect like terms:
7 - 8x - 3x^2
Now where you see an x
replace it with -1
7 - 8x - 3x^2
7 - 8(-1) - 3(-1)^2
7 + 8 -3(1)
7 + 8 - 3
= 12
..........
(fg)(-1)
(2 - x)(3x^2 + 7x -5)
6x^2 + 14x - 10 - 3x^3 - 7x^2 + 5x
Collect like terms:
-10 + 19x - x^2 - 3x^3
Now where you see an x
replace it with -1
-10 +19(-1) -(-1)^2 - 3(-1)^3
-10 -19 -1(1) - 3(-1)
-10 - 19 -1 + 3
= -27
..............
(f - g)(x)
(3x^2 + 7x - 5) -(2 - x)
Your answer was right.
3x^2 + 8x - 7
.............
Hope this helps.
Remember +x+ and -x- = +
+x- and -x+ = -
All the best :-)

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