If f(x)=x2−3x−23 and g(x)=x−1, how do you find (f⋅g)(x)?

2 Answers
Cri007
Apr 24, 2017

See below.

Explanation:

(f⋅g)(x) is the same as f(x)⋅g(x).

Then, this is just:

(x2−3x−23)(x−1)=x3−x2−3x2+3x−23x+23

Combining like terms,

=x3−4x2−20x+23

ceenik
Apr 24, 2017

(f⋅g)(x)=x2−5x−19

Explanation:

When you read (f⋅g)(x) read it as g inside of f.
This means we are taking the value of g and putting it into f

If they told us to solve (g⋅f)(x) it would mean f inside of g and it would look like this:
(g⋅f)(x)=(x2−3x−23)−1

We have:

(f⋅g)(x)=(x−1)2−3(x−1)−23

Exponents first

(f⋅g)(x)=x2−2x+1−3(x−1)−23

Now multiply

(f⋅g)(x)=x2−2x+1−3x+3−23

Organize / Add and subtract common variables

(f⋅g)(x)=x2−5x−19

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