Question

What’s the answer???

Answer 1

`f(x)=(1)/(3x+2)\to y=(1)/(3x+2)\\\\\text{exchange x to y}\\\\x=(1)/(3y+2)\qquad\text{solve for y}\\\\(1)/(3y+2)=x\qquad\text{multiply both sides by}\ 3y+2\\eq0\\\\1=x(3y+2)\qquad\text{divide both sides by }\ x\\eq0\\\\(1)/(x)=3y+2\qquad\text{subtract 2 from both sides}\\\\(1)/(x)-2=3y\qquad\text{divide both sides by 3}\\\\(1)/(3x)-(2)/(3)=y\to y=(1)/(3x)-(2)/(3)`

`Domain:\ 3x\\eq0\to x\\eq0\\Vetical\ asyptote:y=-(2)/(3)\\\\Answer:\\domain\ (-\infty,\ 0)\ \cup\ (0,\ \infty)\\\\range\ \left(-\infty,\ -(2)/(3)\right)\ \cup\ \left(-(2)/(3),\ \infty\right)`