## Book: RS Aggarwal - Mathematics

### Chapter: 3. Functions

#### Subject: Maths - Class 11th

##### Q. No. 1 of Exercise 3C

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##### Find the domain of each of the following real function.(i) (ii) (iii) (iv)

(i)

Given:

Need to find: Where the functions are defined.

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

Therefore,

It means that the denominator is zero when x = 3 and x = -3

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

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

(ii)

Given:

Need to find: Where the functions are defined.

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

Therefore,

&

It means that the denominator is zero when x = 1 and x = -2

So, the domain of the function is the set of all the real numbers except 1 and -2.

The domain of the function, Df(x) = (- ∞, -2) (-2, 1) (1, ∞).

(iii)

Given:

Need to find: Where the functions are defined.

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

Therefore,

&

It means that the denominator is zero when x = 2 and x = 6

So, the domain of the function is the set of all the real numbers except 2 and 6.

The domain of the function, Df(x) = (- ∞, 2) (2, 6) (6, ∞).

(iv)

Given:

Need to find: Where the functions are defined.

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

Therefore,

It means that the denominator is zero when x = -1 and x = 1

So, the domain of the function is the set of all the real numbers except -1 and +1.

The domain of the function, Df(x) = (- ∞, -1) (-1, 1) (1, ∞).

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