Define Domain Math

Introduction to define domain math:

Define domain:

In math, the domain of a function can be defined as the set of all possible input or argument values which allows the functions to be defined. The function provides output value for each input value of the function domain. For example, consider ' f ' be the function between A and B, then A is called the domain of the function ' f '.

Here, we are going to see few example and practice problems of domain which help you for learning domain function in math.

Example Problems to Define Domain in Math:

Define domain math with example problem 1:

Find the domain of the function y = x^2 + 7.

Solution:

Step 1: Given function

y = x^2 + 7 .

Step 2: To find domain

In the given function, the term x^2 is never negative and therefore x^2 + 7 never less than seven.

Hence, the domain is all real numbers greater than 7.

Step 3: Solution

The domain of the given function is all real numbers y ≥ 7.

Define domain math with example problem 2:

Find domain of the function y = |x + 13|.

Solution:

Step 1: Given function

y = |x + 13| .

Step 2: To find domain

We know that the modulus function gives us only positive values.

That is, the domain of modulus function is (0, ∞).


Step 3: Solution

Hence, the domain of the given function is (0, ∞).

Define domain math with example problem 3:

Find domain of the function y = `(11x - 4)/(x^2 + 7x + 12)`

Solution:

Step 1: Given function

y = `(11x - 4)/(x^2 + 7x + 12)`

Step 2: Set the denominator of the given function y = `(11x - 4)/(x^2 + 7x + 12)` to zero and solve for x

x^2 + 7x + 12 = 0

The above equation can be written as

x^2 + 4x + 3x + 12 = 0

By taking common terms outside, we get

x(x + 4) + 3(x + 4) = 0

(x + 3)(x + 4) =0

By factoring each term, we get

x = - 3, x = - 4

Step 3: Solution

Therefore, the domain of a given function is all real numbers except for x = - 3 or -4

Practice Problems to Define Domain in Math:

1) Find domain of the function y = x^2 + 15

2) Find domain of the function y = |7x - 11|

3) Find domain of the function y = `(5x + 9)/(x^2 + 5x + 4)`

Solutions:

1) The domain of the given function is all real numbers greater than 15.

2) The domain of the given function is (0, ∞).

3) The domain of a given function is all real numbers except for x = - 1 or - 4.