Find the domain and the range of each of the following real f(x)=1/x-5 function:
Find the domain and the range of each of the following real f(x)=1/x-5 function:

Answer : Given:

Need to find: Where the functions are defined.

Let,————————– (1)

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

Therefore, x – 5 = 0

⇒ x = 5

It means that the denominator is zero when x = 5

So, the domain of the function is the set of all the real numbers except 5. The domain of the function, Df(x) = (- ∞, 5) ???? (5, ∞).

Now, to find the range of the function we need to interchange x and y in the equation no. (1)

So the equation becomes,

To find the range of the function f(x1) we need to equate the denominator of the function to 0.

Therefore, x = 0

It means that the denominator is zero when x = 0

So, the range of the function is the set of all the real numbers except 0. The range of the function, Rf(x) = (- ∞, 0) ???? (0, ∞).