f(x) = x^2 +1 and g(x) = 3x - 2 find ( f x g) (x)

To find \((f \times g)(x)\), also written as \((f \cdot g)(x)\) or \(f(x) \times g(x)\), you multiply the functions \(f(x)\) and \(g(x)\) together. 

Given:
\[
f(x) = x^2 + 1
\]
\[
g(x) = 3x - 2
\]

The product of the functions is:
\[
(f \times g)(x) = f(x) \times g(x) 
\]

Now, substitute the given functions:
\[
(f \times g)(x) = (x^2 + 1) \times (3x - 2)
\]

Expand this expression by distributing:
\[
(f \times g)(x) = x^2 \times 3x + x^2 \times (-2) + 1 \times 3x + 1 \times (-2)
\]

Simplify:
\[
(f \times g)(x) = 3x^3 - 2x^2 + 3x - 2
\]

So, the final answer is:
\[
(f \times g)(x) = 3x^3 - 2x^2 + 3x - 2
\]

Would you like more details or have any questions?

Here are some related questions:
1. How do you find the sum of two functions, \(f(x) + g(x)\)?
2. What is the process for finding the difference of two functions, \(f(x) - g(x)\)?
3. How do you find the quotient of two functions, \((f/g)(x)\)?
4. How do you find the composite function \((f \circ g)(x)\)?
5. What is the derivative of the product of two functions, using the product rule?

**Tip:** When multiplying polynomials, ensure each term from the first polynomial is multiplied by each term from the second polynomial, then combine like terms.

Learn how to multiply functions f(x) = x^2 + 1 and g(x) = 3x - 2 with a step-by-step solution. This problem involves functions and polynomials, specifically focusing on the multiplication of functions. Suitable for high school students in Grades 10-12.

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