Domain of a Function - Examples, Exercises and Solutions

Select the field of application of the following fraction:

$\frac{8+x}{5}$

Since the domain depends on the denominator, we note that there is no variable in the denominator.

Therefore, the domain is all numbers.

All numbers

Select the field of application of the following fraction:

$\frac{6}{x}$

Since the domain of definition depends on the denominator, and X appears in the denominator

All numbers will be suitable except for 0.

In other words, the domain of definition:

$x\ne0$

All numbers except 0

Given the following function:

$\frac{9x}{4}$

Does the function have a domain? If so, what is it?

Since the function's denominator equals 4, the domain of the function is all real numbers, meaning all X.

No, the entire domain

Given the following function:

$\frac{5+4x}{2+x^2}$

Does the function have a domain? If so, what is it?

Since the denominator is positive for all X, the domain of the function is the entire domain.

That is, all X, therefore there is no domain restriction.

No, the entire domain

Select the field of application of the following fraction:

$\frac{x}{16}$

$All~X$

$2x+\frac{6}{x}=18$

What is the domain of the above equation?

x≠0

$2x-3=\frac{4}{x}$

What is the domain of the exercise?

x≠0

Look at the following function:

$\frac{20}{10x-5}$

What is the domain of the function?

$x\ne\frac{1}{2}$

Look at the following function:

$\frac{2x+2}{3x-1}$

What is the domain of the function?

$x\ne\frac{1}{3}$

Consider the following function:

$\frac{3x+4}{2x-1}$

What is the domain of the function?

$x\ne\frac{1}{2}$

Look at the following function:

$\frac{10x-3}{5x-3}$

What is the domain of the function?

$x\ne\frac{3}{5}$

Look at the following function:

$\frac{2x+2}{9x+6}$

What is the domain of the function?

$x\ne-\frac{2}{3}$

Given the following function:

$\frac{12}{8x-4}$

What is the domain of the function?

$x\ne\frac{1}{2}$

Look the following function:

$\frac{1}{5x-4}$

What is the domain of the function?

$x\ne\frac{4}{5}$

Given the following function:

$\frac{24}{21x-7}$

What is the domain of the function?

$x\ne\frac{1}{3}$