Problemas
Let f(x)=x^3-x and g(x)=x^2+2x-8 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)(-2)=square ((f)/(g))(-2)= square : all real numbers xvert xneq 0 xvert xneq 2,-4 xvert xneq -2,4
Roztwór
Enrique
veterano · Tutor durante 12 años
4.6
(99 Votos)
Respuesta
\((fg)(x) = (x^3 - x) * (x^2 + 2x - 8)\)\((f/g)(x) = (x^3 - x) / (x^2 + 2x - 8)\)The domain of \((fg)(x)\) is all real numbers.The domain of \((f/g)(x)\) is all real numbers except
and
.\((fg)(-2) = (-2^3 - (-2)) * ((-2)^2 + 2*(-2) - 8)\)\((f/g)(-2) = (-2^3 - (-2)) / ((-2)^2 + 2*(-2) - 8)\)
Explicación
## Step 1The problem involves the operations of function multiplication and division. The functions given are \(f(x) = x^3 - x\) and \(g(x) = x^2 + 2x - 8\).## Step 2To find the product of the two functions, we multiply them together. This is represented as \((fg)(x) = f(x) * g(x)\).## 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 two functions, the domain is the set of all real numbers except for those that make the denominator zero.## Step 5To evaluate the product and quotient of the functions at a specific point, we substitute the given x-value into the function.