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, D_{f(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, D_{f(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, D_{f(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, D_{f(x)} = (- ∞, -1) ∪ (-1, 1) ∪ (1, ∞).

1