Given that $y=\frac{2\left( x-3 \right)}{x+1}$ for $x\ne a$, state the value of $a$, determine

Question

Given that $y=\frac{2\left( x-3 \right)}{x+1}$ for $x\ne a$, state the value of $a$, determine if $y$ is an increasing or a decreasing function.

Accepted Answer

(i) $a=-1$. (ii) Increasing on each interval $(-\infty,-1)$ and $(-1,\infty)$, since $y'=\frac8{(x+1)^2}>0$.

Differentiation - Increasing and Decreasing Functions