Examples with solutions for Domain of a Function: Multiple domains

Exercise #1

Find the area of domain (no need to solve)

14x6x=2x5 \frac{14}{x}-6x=\frac{2}{x-5}

Video Solution

Answer

x0,x5 x≠0,x≠5

Exercise #2

Find the area of domain (no need to solve)

9(4x5x)=20(3x6x+1) 9(4x-\frac{5}{x})=20(3x-\frac{6}{x+1})

Video Solution

Answer

x0,x1 x≠0,x≠-1

Exercise #3

Find the domain

(no need to resolve)

5x2(x7)=108x \frac{5x}{2(x-7)}=\frac{10}{8x}

Video Solution

Answer

x0,x7 x≠0,x≠7

Exercise #4

Find the area of domain (no need to solve)

7x+5=613x \frac{7}{x+5}=\frac{6}{13x}

Video Solution

Answer

x0,x5 x≠0,x≠-5

Exercise #5

Find the area of domain (no need to solve)

(4x2)×(7xx6)=2 (\frac{4}{x-2})\times(\frac{7x}{x-6})=2

Video Solution

Answer

x2,x6 x≠2,x≠6

Exercise #6

Look at the following function:

3x2+129 \frac{\sqrt{-3x^2+12}}{9}

What is the domain of the function?

Video Solution

Answer

2x2 -2 \le x \le 2

Exercise #7

Look at the following function:

5x2+210 \frac{\sqrt{5x^2+2}}{10}

What is the domain of the function?

Video Solution

Answer

All real numbers

Exercise #8

Look at the following function:

3x2+712 \frac{\sqrt{3x^2+7}}{12}

What is the domain of the function?

Video Solution

Answer

All real numbers

Exercise #9

Look at the following function:

2.5x255 \frac{\sqrt{2.5x^2-5}}{5}

What is the domain of the function?

Video Solution

Answer

x2,x2 x\ge\sqrt{2},x\le-\sqrt{2}

Exercise #10

Given the following function:

3x2+39 \frac{\sqrt{3x^2+3}}{9}

What is the domain of the function?

Video Solution

Answer

The entire domain

Exercise #11

Look at the following function:

4x2410 \frac{\sqrt{4x^2-4}}{10}

What is the domain of the function?

Video Solution

Answer

x1,x1 x\ge1,x\le-1

Exercise #12

Look at the following function:

4x285 \frac{\sqrt{4x^2-8}}{5}

What is the domain of the function?

Video Solution

Answer

x2,x2 x\ge\sqrt{2},x\le-\sqrt{2}

Exercise #13

Look at the following function:

x2+23 \frac{\sqrt{x^2+2}}{3}

What is the domain of the function?

Video Solution

Answer

All real numbers

Exercise #14

Look at the following function:

x+23x29 \frac{x+2}{\sqrt{3x^2-9}}

What is the domain of the function?

Video Solution

Answer

x>\sqrt{3},x<-\sqrt{3}

Exercise #15

Look at the following function:

8x2x22 \frac{8x}{\sqrt{2x^2-2}}

What is the domain of the function?

Video Solution

Answer

x > 1,x < -1

Exercise #16

Look at the following function:

5x+4x29 \frac{5x+4}{\sqrt{x^2-9}}

What is the domain of the function?

Video Solution

Answer

x > 3,x < -3

Exercise #17

Given the following function:

10x+2x24 \frac{10x+2}{\sqrt{x^2-4}}

What is the domain of the function?

Video Solution

Answer

x > 2,x < -2

Exercise #18

Find the area of domain (no need to solve)

x5x6=2x1 \frac{x}{5x-6}=\frac{2}{x-1}

Video Solution

Answer

x1,x115 x≠1,x≠1\frac{1}{5}

Exercise #19

15+34:z4y12+8:2=5 \frac{\sqrt{15}+34:z}{4y-12+8:2}=5

What is the field of application of the equation?

Video Solution

Answer

y2 y\operatorname{\ne}2

Exercise #20

Does the following equation have a true or false value?

x281(x9)(x+9)=1 \frac{x^2-81}{(x-9)(x+9)}=1

Video Solution

Answer

True only when x±9 x\ne\pm9 .