the domain for f(x) and g(x) is all real numbers. let f(x) = x² + 1 and g(x) = x⁴ - 1. find f·g. a. x⁶ - x² - 1 b. x⁴ + x² - 1 c. x⁶ + x⁴ - x² - 1 d. x⁸ + x⁴ - x² + 1

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Accepted Answer

# Explanation:
## Step1: Recall the product of functions
To find $ f \cdot g $, we need to multiply the two functions $ f(x) $ and $ g(x) $. So, $ (f \cdot g)(x)=f(x)\times g(x) $. Given $ f(x) = x^2 + 1 $ and $ g(x)=x^4 - 1 $, we use the distributive property (FOIL for polynomials).

## Step2: Apply the distributive property
$$
\begin{align*}
(f \cdot g)(x)&=(x^2 + 1)(x^4 - 1)\
&=x^2 \cdot x^4 + x^2 \cdot (-1)+1 \cdot x^4 + 1 \cdot (-1)\
&=x^{2 + 4}-x^2 + x^4 - 1\
&=x^6 + x^4 - x^2 - 1
\end{align*}
$$

# Answer:
C. $ x^6 + x^4 - x^2 - 1 $

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the product of functions

Step2: Apply the distributive property

Answer: