If f(x) = x^2-3x-23 and g(x) = x-1, how do you find (f*g)(x)?

2 Answers
Apr 24, 2017

See below.

Explanation:

(f*g)(x) is the same as f(x)*g(x).

Then, this is just:

(x^2-3x-23)(x-1)=x^3-x^2-3x^2+3x-23x+23

Combining like terms,

=x^3-4x^2-20x+23

Apr 24, 2017

(f*g)(x)=x^2-5x-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)=(x^2-3x-23)-1


We have:

(f*g)(x)=(x-1)^2-3(x-1)-23

Exponents first

(f*g)(x)=x^2-2x+1-3(x-1)-23

Now multiply

(f*g)(x)=x^2-2x+1-3x+3-23

Organize / Add and subtract common variables

(f*g)(x)=x^2-5x-19