Book: RS Aggarwal - Mathematics
Chapter: 3. Functions
Subject: Maths - Class 11th
Q. No. 3 of Exercise 3C
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Find the domain and the range of each of the following real function: 
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, ∞).
