Find the domain and the range of each of the following real f(x)=x-16/x-4 function:
Find the domain and the range of each of the following real f(x)=x-16/x-4 function:

Answer : Given:

Need to find: Where the functions are defined.

To find the domain of the function f(x) we need to equate the denominator of the function to 0.

Therefore, x – 4 = 0

⇒ x = 4

It means that the denominator is zero when x = 4

So, the domain of the function is the set of all the real numbers except 4. The domain of the function, Df(x) = (- ∞, 4) ???? (4, ∞).

Now if we put any value of x from the domain set the output value will be either (-ve) or (+ve), but the value will never be 8

So, the range of the function is the set of all the real numbers except 8. The range of the function, Rf(x) = (-∞, 8) ????(8, ∞).