The value of a stock is represented by the function f(x)=2x+4

Question

. 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+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 .

(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
.

Answer 1

To find the function that represents the value of the stock after the increase and decrease, we will add the increase function \( g(x) \) to the original stock function \( f(x) \) and then subtract the decrease function \( h(x) \).

Given the functions:

• \( f(x) = 2x + 4 \)
• \( g(x) = \sqrt{x} + 1 \)
• \( h(x) = x^3 + 7 \)

The combined function representing the stock value after the increase and decrease is: \[ (f + g - h)(x) = f(x) + g(x) - h(x) \] Substituting the functions: \[ (f + g - h)(x) = (2x + 4) + (\sqrt{x} + 1) - (x^3 + 7) \] Simplifying: \[ = 2x + 4 + \sqrt{x} + 1 - x^3 - 7 \] \[ = -x^3 + 2x + \sqrt{x} - 2 \]

So, we have: \[ (f + g - h)(x) = -x^3 + 2x + \sqrt{x} - 2 \]

Next, we need to determine the domain of this function. The original functions must be considered:

1. For \( f(x) = 2x + 4 \): Domain is all real numbers \( (-\infty, \infty) \).
2. For \( g(x) = \sqrt{x} + 1 \): This function is defined for \( x \geq 0 \).
3. For \( h(x) = x^3 + 7 \): Domain is all real numbers \( (-\infty, \infty) \).

Since \( g(x) \) imposes a restriction, the overall domain will be determined by \( g(x) \), which is:

• \( x \geq 0 \).

Thus, the final answer is:

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