The question specifically asks for an

*algebraic* method, so I'm not sure why the thread has been moved to the Calculus forum.

**Mr F says: Post #3.**
Having said that, it doesn't seem to be that easy to show this result by purely algebraic means. Suppose we start by looking at a simpler result:

*The function cannot take values between –4 and +4.* To see that, notice that

Thus

, which means that y cannot lie between –4 and +4.

Now let's try to use a similar method on the function

. At this point, I will cheat slightly, by using the helpful graph linked to in Mr F's first comment above. That makes it look as though y cannot take values between 2 and 18, or in other words between 10–8 and 10+8. So we should try to prove that

The first step is to calculate

Apart from having

in place of x, the expression in the red parentheses looks just like

So you should be able to complete the argument from there.