Question

Find the domain for the rational function f of x equals quantity x end quantity divided by quantity x minus 5 end quantity.

Answer 1

All real numbers except for 5.

Explanation:

`f(x)=(x)/(x-5)`

The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.

Thus, we need to find the zero(s) of the denominator to determine the domain.

`x-5=0`

`x=5`

Therefore, the domain of the rational function is all real numbers except for 5.

In set builder notation, this is:

`\{x|x\in \mathbb{R}, x\\eq 5\}`