Question

Prove that the function $f\left(x\right)=\frac{x+1}{x+2}$ is increasing function for $x>0$.

Answer 1

Given $f\left(x\right)=\frac{(x+1)}{(x+2)}$

Now, $f^{\prime }\left(x\right)=\frac{(x+2).1-(x+1).1}{(x+2)2}$

$=\frac{1}{(x+2{)}^2}>0$; $\forall x>0$

So, the function $f\left(x\right)$ is an increasing function for $x>0$.