Question

Determine for each x-value whether it is in the domain of f or not. -

Answer 1

Answer:

-7 is in our domain.

0 is in our domain

7 is not in our domain.

Step-by-step explanation:

So we have the rational function:

$f(x)=\frac{x}{x-7}$

The domain restrictions of rational functions are the zeros of the denominator.  In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.

So, solve for the denominator by setting it to 0:

$x-7=0$

Add 7 to both sides:

$x=7$

So, our domain is all real numbers except for 7.

(When x=7, we have 7/0, which is undefined.)

Therefore:

-7 is in our domain.

0 is in our domain

7 is not in our domain.