Can someone explain in detail how these operations go? I am a bit confused by the placement of X because of the variable being X Please see attached question The task is to find \( f + g \), \( f - g \), \( fg \), and \( \frac{f}{g} \) and their domains.Given functions:\[ f(x) = x^2 + x \]\[ g(x) = x^2 \]1. **Addition of functions (\( f + g \)):** \[ (f + g)(x) = f(x) + g(x) = x^2 + x + x^2 = 2x^2 + x \]2. **Subtraction of functions (\( f - g \)):** \[ (f - g)(x) = f(x) - g(x) = x^2 + x - x^2 = x \]3. **Multiplication of functions (\( fg \)):** \[ (fg)(x) = f(x) \cdot g(x) = (x^2 + x) \cdot x^2 = x^4 + x^3 \]4. **Division of functions (\( \frac{f}{g} \)):** \[ \left( \frac{f}{g} \right)(x) = \frac{f(x)}{g(x)} = \frac{x^2 + x}{x^2} = 1 + \frac{1}{x} \] The domain for \(\frac{f}{g}\) excludes \(x = 0\) since division by zero is undefined.**Domains:**- The domains of \( f \), \( g \), \( f+g \), \( f-g \), and \( fg \) are all real numbers (\(\mathbb{R}\)).- The domain of \(\frac{f}{g}\) is all real numbers except \(x = 0\).

Name: Can someone explain in detail how these operations go? I am a bit conf
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Can someone explain in detail how these operations go? I am a bit confused by the placement of X because of the variable being X Please see attached question The task is to find \( f + g \), \( f - g \), \( fg \), and \( \frac{f}{g} \) and their doma