Domain of a Function: Find the domain of the function

Given the following function:

$\frac{5}{x}$

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

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

In other words, $x\ne0$

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.

Yes, $x\ne0$

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:

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

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

The denominator of the function cannot be equal to 0.

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

$(2x-2)^2\ne0$

$2x\ne2$

$x\ne1$

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

Yes, $x\ne1$

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

Given the following function:

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

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

Yes, $x\ne2$

Given the following function:

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

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

Yes, $x\ne-4$

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:

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

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

Yes, $x\ne3$

Given the following function:

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

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

Yes, $x\ne0$

Given the following function:

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

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

Yes, $x\ne-6$