Answer:
(f - g)(x) = -3x² + 5x - 3.
<u>Domain:</u> Interval notation: ( –∞, ∞)
Inequality notation: –∞ < <em>x</em> < ∞
Step-by-step explanation:
Given the subtraction of function operations, (f - g)(x) where: f(x) = 5x - 3, and g(x) = 3x²:
<h2 /><h2><u>
(f - g)(x)</u>
:</h2>
In order to perform the required subtraction between f(x) and g(x), we must subtract the value given in g(x) from f(x).
(f - g)(x) = 5x - 3 - 3x²
Rearrange terms in descending order of degree:
(f - g)(x) = 5x - 3 - 3x² ⇒ -3x² + 5x - 3
Therefore, (f - g)(x) = -3x² + 5x - 3.
<h2 /><h2><u>Domain:</u></h2>
Next, the given prompt requires to find the domain of the result. If you observe its graph, then you'll see that the graph progressively widens toward the negative infinity (–∞). Since the resulting function operations is a downward-facing quadratic function, then it means that its domain values are all real numbers, as there are no domain constraints or undefined points on the graph.
Therefore, the domain of the function, (f - g)(x) = -3x² + 5x - 3 is the set of all real numbers that are common to both f(x) and g(x).
<h3><u>
Domain: </u></h3>
⇒ Interval notation: ( –∞, ∞)
⇒ Inequality notation: –∞ < <em>x</em> < ∞
