Sujetos
Inicio
/
Matemáticas
/
Let F(x)=x^2-14x+48 and G(x)=x^2-x^3 Find (fg)(x) and ((f)/(g))(x) (fg)(x)=square ((f)/(g))(x)=square State the Domain of Each. Domain

Problemas

Let f(x)=x^2-14x+48 and g(x)=x^2-x^3 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 0,-1 Evaluate the following. (fg)(-4)= square ((f)/(g))(-4)= square xvert xneq 0,1

Roztwór

Gerardo maestro · Tutor durante 5 años
Weryfikacja ekspertów
4.4 (388 Votos)

Respuesta

\((fg)(x) = (x^2 - 14x + 48) \cdot (x^2 - x^3)\)\((f/g)(x) = (x^2 - 14x + 48) / (x^2 - x^3)\)Domain of \((fg)(x)\): All real numbersDomain of \((f/g)(x)\): All real numbers except and \((fg)(-4) = (-4)^2 - 14(-4) + 48 \cdot ((-4)^2 - (-4)^3)\)\((f/g)(-4) = ((-4)^2 - 14(-4) + 48) / ((-4)^2 - (-4)^3)\)

Explicación

## Step 1The problem involves the operations of function multiplication and division. The functions given are \(f(x) = x^2 - 14x + 48\) and \(g(x) = x^2 - x^3\).## Step 2To find the product of the two functions, we multiply them together. This is represented as \((fg)(x) = f(x) \cdot g(x)\).## Step 3To find the quotient of the two functions, we divide \(f(x)\) by \(g(x)\). This is represented as \((f/g)(x) = f(x) / g(x)\).## Step 4The 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, the domain is the intersection of the domains of the individual functions.## Step 5The domain of the product \((fg)(x)\) is all real numbers, because both \(f(x)\) and \(g(x)\) are defined for all real numbers.## Step 6The domain of the quotient \((f/g)(x)\) is all real numbers except where the denominator \(g(x)\) equals zero. This is because division by zero is undefined.## Step 7To evaluate \((fg)(-4)\) and \((f/g)(-4)\), we substitute into the expressions for \((fg)(x)\) and \((f/g)(x)\).