Domain of a Function: Find the domain of the function

Finding the Domain of a Square Root FunctionMultiple domainsFind the domain of an expression with fractions
Question 1

Given the following function:

\( \frac{5}{x} \)

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

Question 2

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

\( \frac{9x}{4} \)

Question 3

Given the following function:

\( \frac{5+4x}{2+x^2} \)

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

Question 4

Given the following function:

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

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

Question 5

Given the following function:

\( \frac{23}{5x-2} \)

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

Examples with solutions for Domain of a Function: Find the domain of the function

Exercise #1

Given the following function:

5x \frac{5}{x}

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

Video Solution

Step-by-Step Solution

Since the unknown is in the denominator, we should remember that the denominator cannot be equal to 0.

In other words, x≠0 x\ne0

The domain of the function is all those values that, when substituted into the function, will make the function legal and defined.

The domain in this case will be all real numbers that are not equal to 0.

Answer

Yes, x≠0 x\ne0

Exercise #2

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

9x4 \frac{9x}{4}

Video Solution

Step-by-Step Solution

Since the function's denominator equals 4, the domain of the function is all real numbers. This means that any one of the x values could be compatible.

Answer

No, the entire domain

Exercise #3

Given the following function:

5+4x2+x2 \frac{5+4x}{2+x^2}

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

Video Solution

Step-by-Step Solution

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.

Answer

No, the entire domain

Exercise #4

Given the following function:

65(2x−2)2 \frac{65}{(2x-2)^2}

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

Video Solution

Step-by-Step Solution

The denominator of the function cannot be equal to 0.

Therefore, we will set the denominator equal to 0 and solve for the domain:

(2x−2)2≠0 (2x-2)^2\ne0

2x≠2 2x\ne2

x≠1 x\ne1

In other words, the domain of the function is all numbers except 1.

Answer

Yes, x≠1 x\ne1

Exercise #5

Given the following function:

235x−2 \frac{23}{5x-2}

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

Video Solution

Answer

Yes, x≠25 x\ne\frac{2}{5}

Question 1

Given the following function:

\( \frac{49+2x}{x+4} \)

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

Question 2

Given the following function:

\( \frac{5-x}{2-x} \)

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

Question 3

Given the following function:

\( \frac{8+8x}{(x+6)^2} \)

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

Question 4

Given the following function:

\( \frac{5+4x}{(x-3)^2} \)

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

Question 5

Given the following function:

\( \frac{5+4x}{x^2} \)

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

Exercise #6

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, x≠−4 x\ne-4

Exercise #7

Given the following function:

5−x2−x \frac{5-x}{2-x}

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

Video Solution

Answer

Yes, x≠2 x\ne2

Exercise #8

Given the following function:

8+8x(x+6)2 \frac{8+8x}{(x+6)^2}

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

Video Solution

Answer

Yes, x≠−6 x\ne-6

Exercise #9

Given the following function:

5+4x(x−3)2 \frac{5+4x}{(x-3)^2}

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

Video Solution

Answer

Yes, x≠3 x\ne3

Exercise #10

Given the following function:

5+4xx2 \frac{5+4x}{x^2}

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

Video Solution

Answer

Yes, x≠0 x\ne0