Question

Use the functions below.

f(x)=−2|x+2|−1
g(x)=x2+3
h(x)=4x−2−−−−√3+2
What is (f+g+h)(x)
?

Enter the missing values.

(1 point)
(f+g+h)(x)=
$$

Answer 1

To find \((f+g+h)(x)\), we need to add together the functions \(f(x)\), \(g(x)\), and \(h(x)\).

1. The function \(f(x)\) is given as:
\[
f(x) = -2|x + 2| - 1
\]

2. The function \(g(x)\) is given as:
\[
g(x) = x^2 + 3
\]

3. The function \(h(x)\) is given as:
\[
h(x) = \sqrt{4x - 2} + 3
\]

Now, we add these functions together:

\[
(f + g + h)(x) = f(x) + g(x) + h(x)
\]

Substituting each function into the equation:

\[
(f + g + h)(x) = (-2|x + 2| - 1) + (x^2 + 3) + (\sqrt{4x - 2} + 3)
\]

Combining like terms:

\[
= -2|x + 2| + x^2 + \sqrt{4x - 2} + 3 - 1 + 3
\]
\[
= -2|x + 2| + x^2 + \sqrt{4x - 2} + 5
\]

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

\[
\boxed{-2|x + 2| + x^2 + \sqrt{4x - 2} + 5}
\]