Find the domain for the rational function f of x equals quantity x minus 1 end quantity divided by quantity x plus 3 end quantity. (−[infinity], 1) (1, [infinity]) (−[infinity], −1) (−1, [infinity]) (−[infinity], 3) (3, [infinity]) (−[infinity], −3) (−3, [infinity])
Accepted Solution
A:
Answer:The domain of the function is [tex](-\infty, -3)\cup(-3,\infty)[/tex]Step-by-step explanation:Consider the provided rational function.[tex]f(x)=\frac{x-1}{x+3}[/tex]We need to determine the domain of the rational function.Domain of a rational function is all real numbers except those for which the denominator is 0.The denominator of the rational function is [tex]x+3[/tex]From the above definition we know that:[tex]x+3\neq 0[/tex][tex]x\neq -3[/tex]That means for x=-3 the denominator is 0. Therefore, the domain of the function is all real number except -3.Thus, the domain of the function is [tex](-\infty, -3)\cup(-3,\infty)[/tex]