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, D_{f(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, R_{f(x)} = (- ∞, ) ∪ (, ∞).

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