# How do you find the domain and range of a function?

The domain of a function is the set of all possible inputs for the function and the range of a function in algebra is the set of all its outputs.

## Answer: A domain is ‘all the values’ that go into a function and the range of a function in algebra is the set of all its outputs.

Let's understand about domain and range

**Explanation:**

A domain of a function is the set of all its input values or also defined as all the possible values of the independent variable x (input), for which y (output) is defined.

The range of a given function is the set of all its output values. It is a subset of codomain.

**Finding Domain:**

For a given ordered pair (x,y) the domain is defined as the set of all first elements also known as the inputs of ordered pairs (x-coordinates). Thus, on a function graph, the domain can be found by the set of values towards the direction of the x-axis.

**Finding Range:**

In a given ordered pair (x,y) the range is the set of all second elements of ordered pairs (y-coordinates). On a function graph, the set of values towards the direction of the y-axis is termed as the range.

Let's take an example to understand the calculation of domain and range. We will find the domain and range of the function y = 2− √−3x + 2 algebraically.

**Domain**

The domain of a square root function is defined when the value inside it is a non-negative or a positive number. Hence, the value of -3x + 2 must be a positive number. So for the domain,

−3x + 2 ≥ 0

⇒ −3x ≥ −2

⇒ x ≤ 2 / 3

**Range**

We already know that the square root function results in a non-negative value always.

√−3x + 2 ≥ 0

Multiply with -1 on both sides

⇒ −√−3x + 2 ≤ 0

Adding 2 on both sides,

⇒ 2 − √−3x + 2 ≤ 2

⇒ y ≤ 2

Thus, Domain = {x ∈ R / x ≤ 2/3}

Range = {y ∈ R /y ≤ 2}