Domain of a Function: Find the domain of an expression with fractions

Examples with solutions for Domain of a Function: Find the domain of an expression with fractions

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

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 #5

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 #6

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 #7

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}

Exercise #8

Look at the following function:

10x35x3 \frac{10x-3}{5x-3}

What is the domain of the function?

Video Solution

Answer

x35 x\ne\frac{3}{5}

Exercise #9

Consider the following function:

3x+42x1 \frac{3x+4}{2x-1}

What is the domain of the function?

Video Solution

Answer

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

Exercise #10

Look at the following function:

2010x5 \frac{20}{10x-5}

What is the domain of the function?

Video Solution

Answer

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

Exercise #11

Look at the following function:

2x+23x1 \frac{2x+2}{3x-1}

What is the domain of the function?

Video Solution

Answer

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

Exercise #12

Look at the following function:

5x+24x3 \frac{5x+2}{4x-3}

What is the domain of the function?

Video Solution

Answer

x34 x\ne\frac{3}{4}

Exercise #13

22(2x1)=30 22(\frac{2}{x}-1)=30

What is the domain of the equation above?

Video Solution

Answer

x≠0

Exercise #14

2x3=4x 2x-3=\frac{4}{x}

What is the domain of the exercise?

Video Solution

Answer

x≠0

Exercise #15

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

What is the domain of the above equation?

Video Solution

Answer

x≠0

Exercise #16

What is the domain of the exercise?

5x+82x6=30 \frac{5x+8}{2x-6}=30

Video Solution

Answer

x≠3

Exercise #17

Given the following function:

65(2x2)2 \frac{65}{(2x-2)^2}

What is the domain of the function?

Video Solution

Answer

x1 x\ne1

Exercise #18

Given the following function:

8x212 \frac{8}{x-2\frac{1}{2}}

What is the domain of the function?

Video Solution

Answer

x212 x\ne2\frac{1}{2}

Exercise #19

Look at the following function:

4x+4x18 \frac{4x+4}{x-\frac{1}{8}}

What is the domain of the function?

Video Solution

Answer

x18 x\ne\frac{1}{8}

Exercise #20

Given the following function:

5x+1510x+12 \frac{5x+15}{10x+\frac{1}{2}}

What is the domain of the function?

Video Solution

Answer

x120 x\ne-\frac{1}{20}