precalculus help

Question

Answer 1

Often times. it is easier to determine what values of "x" cannot be used. In the case of rational expressions, there is a rule in math that governs: Division by zero is undefined, therefore, if you can find a value for "x" that results in dividing by zero, that value produces a situation that is not defined, or, in other words, is not allowed.

In this case, if x - 7 = 0, then we would have that situation that is undefined or not allowed.

So x - 7 cannot equal zero:

x - 7 ≠ 0

x ≠ 7

Answer 2

The domain of the function consists of all real numbers, excluding any value(s) of x for which the denominator is zero.