Indefinite integral - Examples, Exercises and Solutions

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

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

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?

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

Given the following function:

$\frac{5}{x}$

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

Yes, $x\ne0$

Given the following function:

$\frac{23}{5x-2}$

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

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

Given the following function:

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

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

Yes, $x\ne-4$