Question

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) ?

Answer 1

The domain of h(x) = f(x) /g(x) will be all real numbers without -6 because for -6 will result the denominator equal zero and hence this fraction will be undefined 

Answer 2

Answer:

Domain is the set of all possible values of x where function is defined.

As per the statement:

The domain of both f(x) = x - 6 and g(x) = x + 6 is all real numbers.

We have to find the domain of  $h(x) = \frac{f(x)}{g(x)}$;

$h(x) = \frac{f(x)}{g(x)}$

⇒$h(x) = \frac{x-6}{x+6}$

To find the domain of the given rational function.

Exclude the value of x for which function is not defined.

Set denominator = 0

x+6 = 0

x = -6

therefore, the function is defined for all real number except at x = -6.

i.e, {x | x ≠ -6}