Question

Use the functions below.

f(x)=x2+1

g(x)=3x−1

h(x)=|x|+2

What is (f⋅g+h)(x)
?

Enter the missing values.

(1 point)
$$

Answer 1

To find \((f \cdot g + h)(x)\), we will first determine \(f(x)\), \(g(x)\), and \(h(x)\), and then combine them accordingly.

1. We have:

\[
f(x) = x^2 + 1
\]

\[
g(x) = 3x - 1
\]

\[
h(x) = |x| + 2
\]

2. Next, we calculate \(f \cdot g\):

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

To multiply these two functions, we distribute:

\[
(x^2 + 1)(3x - 1) = x^2 \cdot 3x + x^2 \cdot (-1) + 1 \cdot 3x + 1 \cdot (-1)
\]

This simplifies to:

\[
3x^3 - x^2 + 3x - 1
\]

3. Now, we add \(h(x)\) to \(f \cdot g\):

\[
(f \cdot g + h)(x) = (3x^3 - x^2 + 3x - 1) + (|x| + 2)
\]

Combining terms gives us:

\[
3x^3 - x^2 + 3x - 1 + |x| + 2
\]

Which simplifies to:

\[
3x^3 - x^2 + 3x + |x| + 1
\]

So, the final expression for \((f \cdot g + h)(x)\) is:

\[
3x^3 - x^2 + 3x + |x| + 1
\]

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