f(x)=x^2-16 and g(x)=x+4 find f/g and its domain.
follow my method I used in the previous one.
x^2 - 16 factors as a difference of squares
don't forget the restriction
To find the quotient of two functions, f(x) and g(x), you need to divide f(x) by g(x). In this case, f(x) = x^2 - 16 and g(x) = x + 4.
To find f/g, divide the function f(x) by g(x), which can be expressed as (f/g)(x) = f(x) / g(x). So, let's substitute the given functions into the equation:
(f/g)(x) = (x^2 - 16) / (x + 4)
Now, let's find the domain of the function. The domain of (f/g)(x) is the set of all real numbers x for which g(x) is not equal to zero. In other words, we need to find the values of x that make the denominator, x + 4, equal to zero.
x + 4 = 0
x = -4
Since x = -4 makes the denominator zero, it is not included in the domain. Therefore, the domain of (f/g)(x) is all real numbers except x = -4.