Question

The value of a stock is represented by the function f(x)=2x+4
. The function g(x)=x−−√+1
represents an increase in the stock. The function h(x)=x3+7
represents a decrease in the stock. What function represents the value of the stock after the increase and decrease? What is the domain?(1 point)
Responses

(f+g+h)(x)=2x+x−−√+x3+12
and the domain is (−∞,∞)
.
open paren f plus g plus h close paren times x is equal to 2 to the x th power plus square root of x plus x cubed plus 12 and the domain is open paren negative infinity comma infinity close paren .

(f+g−h)(x)=2x+x−−√−x3−2
and the domain is (−∞,∞)
.
open paren f plus g minus h close paren times x is equal to 2 to the x th power plus square root of x minus x cubed minus 2 and the domain is open paren negative infinity comma infinity close paren .

(f+g−h)(x)=2x+x−−√−x3−2
and the domain is x≥0
.
open paren f plus g minus h close paren times x is equal to 2 to the x th power plus square root of x minus x cubed minus 2 and the domain is x is greater than or equal to 0 .

(f+g+h)(x)=2x+x−−√+x3+12
and the domain is x≥0
.
open paren f plus g plus h close paren times x is equal to 2 to the x th power plus square root of x plus x cubed plus 12 and the domain is x is greater than or equal to 0 .

Answer 1

To find the function representing the value of the stock after the increase and decrease, we need to correctly combine the functions \(f(x)\), \(g(x)\), and \(h(x)\).

1. The value of the stock is given by:
\[
f(x) = 2x + 4
\]

2. The increase in the stock is represented by:
\[
g(x) = \sqrt{x} + 1
\]

3. The decrease in the stock is represented by:
\[
h(x) = x^3 + 7
\]

To find the combined function that represents the value of the stock after the increase and decrease, we will calculate:
\[
(f + g - h)(x) = f(x) + g(x) - h(x)
\]

Substituting in the functions:
\[
(f + g - h)(x) = (2x + 4) + (\sqrt{x} + 1) - (x^3 + 7)
\]

Now, combine these terms:
\[
= 2x + 4 + \sqrt{x} + 1 - x^3 - 7
\]
\[
= 2x + \sqrt{x} - x^3 - 2
\]

The resulting function is:
\[
(f + g - h)(x) = 2x + \sqrt{x} - x^3 - 2
\]

Next, we need to find the domain. The function \(g(x) = \sqrt{x} + 1\) has a domain of \(x \geq 0\) because we cannot take the square root of negative numbers. The other functions \(f(x)\) and \(h(x)\) are defined for all real numbers but we must consider the most restricted domain, which is given by \(g(x)\).

Thus, the domain is:
\[
x \geq 0
\]

Therefore, the correct option is:
\[
(f + g - h)(x) = 2x + \sqrt{x} - x^3 - 2 \text{ and the domain is } x \geq 0.
\]