RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 3. Functions

Subject: Maths - Class 11th

Q. No. 13 of Exercise 3C

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13

Find the domain and the range of each of the following real function:

Given:


Need to find: Where the functions are defined.


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


Therefore,


x – 4 = 0


x = 4


It means that the denominator is zero when x = 4


So, the domain of the function is the set of all the real numbers except 4.


The domain of the function, Df(x) = (- ∞, 4) (4, ∞).


The numerator is an absolute function of the denominator. So, for any value of x from the domain set, we always get either +1 or -1 as the output. So, the range of the function is a set containing -1 and +1


Therefore, the range of the function, Rf(x) = { -1 , 1 }


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