Question

1. find the domain of the rational function. express your answer in set builder notation.

$f(x)=\frac{x+1}{(x+3)(x-4)}$

Explanation:

Step1: Identify denominator restriction

A rational function is undefined when its denominator equals 0. So set the denominator equal to 0:
$$(x+3)(x-4) = 0$$

Step2: Solve for x values

Use the zero product property: if $ab=0$, then $a=0$ or $b=0$.
$x+3=0 \implies x=-3$
$x-4=0 \implies x=4$

Step3: Define valid x values

The domain includes all real numbers except $x=-3$ and $x=4$.

Answer:

$\{x \mid x \text{ is a real number, } x
eq -3, x
eq 4\}$