Find the domain and the range of each of the following real function: f(x) =
Given: f(x) =
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,
cx – d = 0
⇒ x =
It means that the denominator is zero when x =
So, the domain of the function is the set of all the real numbers except d/c.
The domain of the function, Df(x) = (- ∞, ) ∪ (, ∞).
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(x) we need to equate the denominator of the function to 0.
Therefore,
⇒
It means that the denominator is zero when x =
So, the range of the function is the set of all the real numbers except a/c.
The range of the function, Rf(x) = (- ∞, ) ∪ (, ∞).