Question
Use the functions below.
f(x)=x2−9
g(x)=x2−x−12
What is (fg)(x)
?
Enter the missing values.
(1 point)
(fg)(x)=
$$
f(x)=x2−9
g(x)=x2−x−12
What is (fg)(x)
?
Enter the missing values.
(1 point)
(fg)(x)=
$$
Answers
GPT-4o mini
To find \((fg)(x)\), we need to multiply the functions \(f(x)\) and \(g(x)\).
Given:
- \(f(x) = x^2 - 9\)
- \(g(x) = x^2 - x - 12\)
Now, we calculate \((fg)(x)\):
\[
(fg)(x) = f(x) \cdot g(x) = (x^2 - 9)(x^2 - x - 12)
\]
To perform the multiplication, we will use the distributive property (also known as the FOIL method for binomials):
\[
(fg)(x) = (x^2)(x^2) + (x^2)(-x) + (x^2)(-12) + (-9)(x^2) + (-9)(-x) + (-9)(-12)
\]
Calculating each term:
1. \(x^2 \cdot x^2 = x^4\)
2. \(x^2 \cdot -x = -x^3\)
3. \(x^2 \cdot -12 = -12x^2\)
4. \(-9 \cdot x^2 = -9x^2\)
5. \(-9 \cdot -x = 9x\)
6. \(-9 \cdot -12 = 108\)
Now, combine all the terms:
\[
(fg)(x) = x^4 - x^3 - 12x^2 - 9x^2 + 9x + 108
\]
Combine like terms:
\[
= x^4 - x^3 - 21x^2 + 9x + 108
\]
So the final answer is:
\[
(fg)(x) = x^4 - x^3 - 21x^2 + 9x + 108
\]
Enter the missing values:
\[
(fg)(x) = x^4 - x^3 - 21x^2 + 9x + 108
\]
Given:
- \(f(x) = x^2 - 9\)
- \(g(x) = x^2 - x - 12\)
Now, we calculate \((fg)(x)\):
\[
(fg)(x) = f(x) \cdot g(x) = (x^2 - 9)(x^2 - x - 12)
\]
To perform the multiplication, we will use the distributive property (also known as the FOIL method for binomials):
\[
(fg)(x) = (x^2)(x^2) + (x^2)(-x) + (x^2)(-12) + (-9)(x^2) + (-9)(-x) + (-9)(-12)
\]
Calculating each term:
1. \(x^2 \cdot x^2 = x^4\)
2. \(x^2 \cdot -x = -x^3\)
3. \(x^2 \cdot -12 = -12x^2\)
4. \(-9 \cdot x^2 = -9x^2\)
5. \(-9 \cdot -x = 9x\)
6. \(-9 \cdot -12 = 108\)
Now, combine all the terms:
\[
(fg)(x) = x^4 - x^3 - 12x^2 - 9x^2 + 9x + 108
\]
Combine like terms:
\[
= x^4 - x^3 - 21x^2 + 9x + 108
\]
So the final answer is:
\[
(fg)(x) = x^4 - x^3 - 21x^2 + 9x + 108
\]
Enter the missing values:
\[
(fg)(x) = x^4 - x^3 - 21x^2 + 9x + 108
\]