RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 3. Functions

Subject: Maths - Class 11th

Q. No. 14 of Exercise 3C

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14

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 – 3 = 0


x = 3


It means that the denominator is zero when x = 3


So, the domain of the function is the set of all the real numbers except 3.


The domain of the function, Df(x) = (- ∞, 3) (3, ∞).


Now if we put any value of x from the domain set the output value will be either (-ve) or (+ve), but the value will never be 6


So, the range of the function is the set of all the real numbers except 6.


The range of the function, Rf(x) = (-∞, 6) (6, ∞).


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