HOW TO FIND THE DOMAIN OF A FUNCTION IN INTERVAL NOTATION

Find the domain of each of the following functions. Then express your answer in interval notation.

Problem 1 :

Solution:

To find for what values of x the function is defined, first we have to check for what values of x the function is undefined.

For that, we have to equate the denominator to 0. 

x - 3 = 0

x = 3

The domain is all real values except 3.

 x ≠ 3

Interval Notation:

(-∞, 3) ∪ (3, +∞)

Problem 2 :

Solution:

For what value of x the function is defined, first we have to check for what values of x the function is undefined.

For that, we have to equate the denominator to 0. 

x² - 9 = 0

x² = 9

x = ± 3

The domain is all real values except 3 and -3.

  x ≠ 3 and x ≠ -3

Interval Notation:

(-∞, -3) ∪ (-3, 3) ∪ (3, +∞)

Problem 3 :

Solution:

For what value of x the function is defined, first we have to check for what values of x the function is undefined.

For that, we have to equate the denominator to 0. 

x² - 11x + 28 = 0

(x - 4) (x - 7) = 0

x - 4 = 0 or x - 7 = 0

x = 4 or x = 7

The domain is all real values except 4 and 7.

  x ≠ 4 and x ≠ 7

Interval Notation:

(-∞, 4) ∪ (4, 7) ∪ (7, +∞)

Problem 4 :

f(t) = √t

Solution:

f(t) = √t

t ≥ 0

Interval Notation:

[0, ∞)

Problem 5 :

Solution:

Interval Notation:

(-∞, ∞)

Problem 6 :

Solution:

For what value of x the function is defined, first we have to check for what values of x the function is undefined.

x - 5 = 0

x = 5

x ≥ 5

Interval Notation:

[5, ∞)

Problem 7 :

Solution:

Interval Notation: