Book: RS Aggarwal - Mathematics

Chapter: 3. Functions

Subject: Maths - Class 11th

Q. No. 8 of Exercise 3C

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8
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) = (- ∞, ) (, ∞).

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