The domain of both f(x) = x - 6 and g(x) = x + 6 is all real numbers. What is the domain of h(x) = f(x)/g(x)?

Solution:

The domain is the set of all possible values of x for a function f(x) where the function is defined.

Given, the domain of both f(x) = x - 6 and g(x) = x + 6 are all real numbers.

To find the domain if h(x) = f(x) / g(x)

⇒ h(x) = (x - 6)/(x + 6)

h(x) cannot exist if g(x) is 0.

Let the denominator of the above rational number be 0.

x + 6 = 0

x = -6

The value of x for which function is not defined is -6.

Therefore, the function is defined for all real numbers except at x = -6

The domain of both f(x) = x - 6 and g(x) = x + 6 is all real numbers. What is the domain of h(x) = f(x)/g(x)?

Summary:

The domain of the function h(x) = f(x) / g(x) is {x | x ≠ -6}.