RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 3. Functions

Subject: Maths - Class 11th

Q. No. 5 of Exercise 3C

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5

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 + 2 = 0


x = -2


It means that the denominator is zero when x = -2


So, the domain of the function is the set of all the real numbers except -2.


The domain of the function, Df(x) = (- ∞, -2) (-2, ∞).


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,


3 – x = 0


x = 3


It means that the denominator is zero when x = 3


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


The range of the function, Rf(x) = (- ∞, 3) (3, ∞).


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