Q. 34.8( 5 Votes )

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

Answer :

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 – 5 = 0

⇒ x = 5

It means that the denominator is zero when x = 5

So, the domain of the function is the set of all the real numbers except 5.

The domain of the function, D_{f(x)} = (- ∞, 5) ∪ (5, ∞).

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(x_{1}) we need to equate the denominator of the function to 0.

Therefore,

x = 0

It means that the denominator is zero when x = 0

So, the range of the function is the set of all the real numbers except 0.

The range of the function, R_{f(x)} = (- ∞, 0) ∪ (0, ∞).

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