Let f(x)=x^2+9x+20 and g(x)=x^3-4x 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 : all real numbers xvert xneq 0 xvert xneq -2,0,2 xvert xneq 0,2 Evaluate the following. (fg)(-1)=square ((f)/(g))(-1)=square

## Step 1<br />The problem involves the operations of function multiplication and division. The functions given are \(f(x) = x^2 + 9x + 20\) and \(g(x) = x^3 - 4x\).<br /><br />## Step 2<br />To find the product of the two functions, we multiply them together. This is represented as \((fg)(x) = f(x) \cdot g(x)\).<br /><br />## Step 3<br />To find the quotient of the two functions, we divide \(f(x)\) by \(g(x)\). This is represented as \((f/g)(x) = f(x) / g(x)\).<br /><br />## Step 4<br />The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the product and quotient of two functions, the domain is the intersection of the domains of the individual functions.<br /><br />## Step 5<br />The domain of the product \((fg)(x)\) is all real numbers, because both \(f(x)\) and \(g(x)\) are defined for all real numbers.<br /><br />## Step 6<br />The domain of the quotient \((f/g)(x)\) is all real numbers except for those that make the denominator zero. In this case, \(g(x) = x^3 - 4x = 0\) when \(x = 0\), \(x = 2\), or \(x = -2\). Therefore, the domain of \((f/g)(x)\) is all real numbers except \(x = 0\), \(x = 2\), and \(x = -2\).<br /><br />## Step 7<br />To evaluate \((fg)(-1)\) and \((f/g)(-1)\), we substitute \(x = -1\) into the expressions for \((fg)(x)\) and \((f/g)(x)\).