f(x)=v^2+13/v^2-4v-32
Find all numbers that are not in the domain of the function. Then give the domain in set notation.
set denominator equal to 0 and solve for x which would make the equation undefined
v^2-4v-32=0
(v-8)(v+4)=0
v=8, v=-4
x is not equal to 8 or -4
The denominator cannot be zero, so find the roots of the denominator.
(v-8)*(v+4)=0
so v cannot be 8, or -4
To find the numbers that are not in the domain of the function f(x), we need to look for any values of x that make the denominator of the function equal to zero, because dividing by zero is undefined.
In this case, the denominator is v^2 - 4v - 32. We can find the values of v that make this denominator equal to zero by setting it equal to zero and solving for v.
v^2 - 4v - 32 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use factoring:
(v - 8)(v + 4) = 0
Setting each factor equal to zero:
v - 8 = 0 or v + 4 = 0
Solving for v:
v = 8 or v = -4
Therefore, the values of v that make the denominator zero are v = 8 and v = -4. These are the numbers that are not in the domain of the function f(x).
To express the domain of the function f(x) in set notation, we can say:
Domain: {v | v ≠ 8, v ≠ -4}
This means that the domain of the function f(x) consists of all values of v except 8 and -4.