"The terms of the sequence $x_0,x_1,\ldots$ satisfy
for $n\geq 0$. Prove that is $x_0>3$ then the sequence is strictly increasing."
I am very stuck on dealing with the inequality here. I know I have to use proof by induction but I cannot even figure out how to show that $x_1$ is greater than $x_0$. I was thinking about doing this graphically, but the problem is that when I sketch this as a function, I know that what I am looking for is that $f(x)$ is above $y=x$ for values of $x$ greater than $3$, but the whole graph is actually above or touching $y=x$, which makes no sense to me because surely for values of $x$ less than $3$ the sequence is decreasing, so the function should lie below the $y=x$ line...
Any ideas would be much appreciated!