Question

What is the vertical asymptotes of the function f(x)=x-2/x*2-3x-4

Answer 1

Answer:

x = -1 and x = 4

Step-by-step explanation:

$f(x)=\dfrac{x-2}{x^2-3x-4}\\\\\text{DOMAIN}:\\\\x^2-3x-4\neq0\\\\x^2-4x+x-4\neq0\\\\x(x-4)+1(x-4)\neq0\\\\(x-4)(x+1)\neq0\iff x-4\neq0\ \wedge\ x+1\neq0\\\\x\neq4\ \wedge\ x\neq-1\\\\\text{Therefore the vertical asymptotes are:}\\\\x=-1\ and\ x=4.$