Let f(x)=x^2-2x-3 and g(x)=x^2-4 .Find (fg)(x) and ((f)/(g))(x) (fg)(x)=square ((f)/(g))(x)=square State the domain of each. Domain of (fg)(x) square Domain of ((f)/(g))(x) square Evaluate the following. (fg)(-3)=square ((f)/(g))(-3)= square : all real numbers xvert xneq 0 xvert xneq -2,2 xvert xneq 2

To find \((fg)(x)\) and \(\left(\frac{f}{g}\right)(x)\), we need to perform the following operations:1. **Find \((fg)(x)\):** To multiply these polynomials, use the distributive property (also known as FOIL for binomials): Calculate each term: Combine all terms: Simplify by combining like terms: So, \((fg)(x) = x^4 - 2x^3 - 7x^2 + 8x + 12\).2. **Find \(\left(\frac{f}{g}\right)(x)\):** The expression is already simplified.3. **State the domain of each:** - The domain of \((fg)(x)\) is all real numbers because it is a polynomial function. Therefore, the domain is: - The domain of \(\left(\frac{f}{g}\right)(x)\) excludes values that make the denominator zero. Solve : This gives and . Therefore, the domain is: 4. **Evaluate the following:** - \((fg)(-3)\): Substitute into \((fg)(x)\): Calculate each term: Add them up: So, \((fg)(-3) = 60\). - \(\left(\frac{f}{g}\right)(-3)\): Substitute into \(\left(\frac{f}{g}\right)(x)\): Calculate the numerator and denominator: Therefore: In summary:- \((fg)(x) = x^4 - 2x^3 - 7x^2 + 8x + 12\)- \(\left(\frac{f}{g}\right)(x) = \frac{x^2 - 2x - 3}{x^2 - 4}\)- Domain of \((fg)(x)\): all real numbers- Domain of \(\left(\frac{f}{g}\right)(x)\): - \((fg)(-3) = 60\)- \(\left(\frac{f}{g}\right)(-3) = \frac{12}{5}\)