Use the functions below.

Question

f(x)=−5x2+4
g(x)=−4x2−7x+9
h(x)=2x2+x−2
What is (f−g−h)(x)
? What is the domain of (f−g−h)(x)
?

(1 point)
Responses

(f−g−h)(x)=−3x2+6x−3
and the domain of (f−g−h)(x)
is x≥4
.
open paren f minus g minus h close paren times x is equal to negative 3 x squared plus 6 x minus 3 and the domain of open paren f minus g minus h close paren times x is x is greater than or equal to 4 .

(f−g−h)(x)=−7x2−6x+11
and the domain of (f−g−h)(x)
is (−∞,∞)
.
open paren f minus g minus h close paren times x is equal to negative 7 x squared minus 6 x plus 11 and the domain of open paren f minus g minus h close paren times x is open paren negative infinity comma infinity close paren .

(f−g−h)(x)=−7x2−6x+11
and the domain of (f−g−h)(x)
is x≥4
.
open paren f minus g minus h close paren times x is equal to negative 7 x squared minus 6 x plus 11 and the domain of open paren f minus g minus h close paren times x is x is greater than or equal to 4 .

(f−g−h)(x)=−3x2+6x−3
and the domain of (f−g−h)(x)
is (−∞,∞)
.
open paren f minus g minus h close paren times x is equal to negative 3 x squared plus 6 x minus 3 and the domain of open paren f minus g minus h close paren times x is open paren negative infinity comma infinity close paren .
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Answer 1

To find \((f - g - h)(x)\), we need to calculate \(f(x) - g(x) - h(x)\).

Given the functions:

• \( f(x) = -5x^2 + 4 \)
• \( g(x) = -4x^2 - 7x + 9 \)
• \( h(x) = 2x^2 + x - 2 \)

Let's perform the calculation step-by-step:

1. Calculate \(f(x) - g(x)\): \[ f(x) - g(x) = (-5x^2 + 4) - (-4x^2 - 7x + 9) \] This simplifies to: \[ -5x^2 + 4 + 4x^2 + 7x - 9 = (-5x^2 + 4x^2) + 7x + (4 - 9) = -x^2 + 7x - 5 \]

2. Now, subtract \(h(x)\): \[ (f(x) - g(x)) - h(x) = (-x^2 + 7x - 5) - (2x^2 + x - 2) \] This simplifies to: \[ -x^2 + 7x - 5 - 2x^2 - x + 2 = (-x^2 - 2x^2) + (7x - x) + (-5 + 2) = -3x^2 + 6x - 3 \]

So, we find that: \[ (f - g - h)(x) = -3x^2 + 6x - 3 \]

3. Now, let's determine the domain of \((f - g - h)(x)\): Since \(f(x)\), \(g(x)\), and \(h(x)\) are all polynomials, their domain is all real numbers. Consequently, the domain of \((f - g - h)(x)\) is also all real numbers.

Thus, the correct response is: \[ (f - g - h)(x) = -3x^2 + 6x - 3 \quad \text{and the domain of } (f - g - h)(x) \text{ is } (-\infty, \infty). \]

So the correct option is: \[ (f - g - h)(x) = -3x^2 + 6x - 3 \text{ and the domain of } (f - g - h)(x) \text{ is } (-\infty, \infty). \]