Domain of a Function - Examples, Exercises and Solutions

The domain of a function includes all those values of X X (independent variable) that, when substituted into the function, keep the function valid and defined.

The domain of a function is an integral part of function analysis. Moreover, a definition set is required to create a graphical representation of the function.

Suggested Topics to Practice in Advance

  1. Ways to represent a function
  2. Representing a Function Verbally and with Tables
  3. Graphical Representation of a Function
  4. Algebraic Representation of a Function
  5. Notation of a Function
  6. Rate of Change of a Function
  7. Variation of a Function
  8. Rate of change represented with steps in the graph of the function
  9. Rate of change of a function represented graphically
  10. Constant Rate of Change
  11. Variable Rate of Change
  12. Rate of Change of a Function Represented by a Table of Values
  13. Functions for Seventh Grade
  14. Increasing and Decreasing Intervals (Functions)
  15. Increasing functions
  16. Decreasing function
  17. Constant Function
  18. Decreasing Interval of a function
  19. Increasing Intervals of a function

Practice Domain of a Function

Exercise #1

6x+5=1 \frac{6}{x+5}=1

What is the field of application of the equation?

Video Solution

Answer

x5 x\operatorname{\ne}-5

Exercise #2

x+y:32x+6=4 \frac{x+y:3}{2x+6}=4

What is the field of application of the equation?

Video Solution

Answer

x3 x\operatorname{\ne}-3

Exercise #3

3x:4y+6=6 \frac{3x:4}{y+6}=6

What is the field of application of the equation?

Video Solution

Answer

y6 y\operatorname{\ne}-6

Exercise #4

Select the field of application of the following fraction:

x16 \frac{x}{16}

Video Solution

Answer

All X All~X

Exercise #5

Select the field of application of the following fraction:

8+x5 \frac{8+x}{5}

Video Solution

Answer

All numbers

Exercise #1

Select the field of application of the following fraction:

6x \frac{6}{x}

Video Solution

Answer

All numbers except 0

Exercise #2

Given the following function:

5x2x \frac{5-x}{2-x}

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

Video Solution

Answer

Yes, x2 x\ne2

Exercise #3

Given the following function:

49+2xx+4 \frac{49+2x}{x+4}

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

Video Solution

Answer

Yes, x4 x\ne-4

Exercise #4

Given the following function:

235x2 \frac{23}{5x-2}

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

Video Solution

Answer

Yes, x25 x\ne\frac{2}{5}

Exercise #5

Given the following function:

9x4 \frac{9x}{4}

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

Video Solution

Answer

No, the entire domain

Exercise #1

Given the following function:

5x \frac{5}{x}

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

Video Solution

Answer

Yes, x0 x\ne0

Exercise #2

Given the following function:

2421x7 \frac{24}{21x-7}

What is the domain of the function?

Video Solution

Answer

x13 x\ne\frac{1}{3}

Exercise #3

Look the following function:

15x4 \frac{1}{5x-4}

What is the domain of the function?

Video Solution

Answer

x45 x\ne\frac{4}{5}

Exercise #4

Given the following function:

128x4 \frac{12}{8x-4}

What is the domain of the function?

Video Solution

Answer

x12 x\ne\frac{1}{2}

Exercise #5

Look at the following function:

2x+29x+6 \frac{2x+2}{9x+6}

What is the domain of the function?

Video Solution

Answer

x23 x\ne-\frac{2}{3}

Topics learned in later sections

  1. Indefinite integral
  2. Inputing Values into a Function