As long as g(x)=x+8-a/x is the increasing function on [1, +∞).

That is g'(x)= 1+a/x? =(x？ +a)/x？ ≥0 holds.

It is known that x≥ 1.

And then x? +a≥0 holds.

Only x= 1 is needed to satisfy the condition.

So 1+a≥0.

The solution is a≥- 1

I hope I can help you O(∩_∩)O