SOLUTION: Let f(x) = 2x + 1 and g(x) = x^2 - 4 and find the following: (fg)(x) (g of f)(x)

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Question 35505This question is from textbook
: Let f(x) = 2x + 1 and g(x) = x^2 - 4 and find the following:
(fg)(x)
(g of f)(x) This question is from textbook

Found 3 solutions by Nate, narayaba, rapaljer:
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website!
f(x) = 2x + 1
g(x) = x^2 - 4
........................................................................
(fg)(x)=(2x+1)(x^2-4)=2x^3+x^2-8x-4
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(g of f)(x) = (2x+1)^2 - 4
= (2x+1)(2x+1) - 4 = 4x^2 + 4x + 1 - 4 = 4x^2 + 4x - 3

Answer by narayaba(40)   (Show Source):
You can put this solution on YOUR website!
Let f(x) = 2x + 1 and g(x) = x^2 - 4
(fg)(x) has two meanings whether it is component wise multiplication or composition
if it is multiplication then (fg)(x) = f(x)*g(x) and if it is composition then (fg)(x) = f(g(x)). There are condition underwhich each of the above is valid
I am assuming it is multiplication here
(fg)(x) = f(x)*g(x) = (2x + 1)*(x^2 - 4) = 2x^3 + x^2 -8x -4

(f-g)(x) = f(x) - g(x) = 2x + 1 - (x^2 - 4) = 2x + 1 - x^2 + 4= -x^2 + 2x + 5

Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website!
The first is just multiplication!
(fg)(x) = f(x) * g(x) = (2x+1)*(x^2-4)

The second is subsitution:
(g of f)(x)

First,
g(x) = x^2 - 4
g(SUB) = (SUB)^2 - 4
g(_____) = (_____)^2 - 4
g( f(x) ) = ( 2x+1)^2 - 4
g( f(x) ) = 4x^2 + 4x + 1 - 4 = 4x^2 + 4x -3

R^2 at SCC