Question

If f(x)=sqrtx for x>0, then, for x>a>0,

f(x)-f(a)/x-a is what?

Answer 1

\[\frac{ f(x)-f(a) }{ x-a}\]

Answer 2

If f(x)=\[\sqrt{x}\]

Answer 3

Do I multiply by the conjugate even though it is on the top?

Answer 4

Well let's see if it helps. \[\frac{\sqrt x-\sqrt a}{x-a}=\frac{x-a}{(x-a)(\sqrt x-\sqrt a)}=\frac{1}{\sqrt x-\sqrt a}\]

Answer 5

@KingGeorge why we do that step?

Answer 6

Well, depending on what you want to do with it, this might be a better way to write it.

What step?

Answer 7

So if the sqrt is always on the top, or bottom, I still have to do the conjugate?

Answer 8

Well, it depends what you want to do with it. Judging by what we're trying to simplify here, the form with the roots on the bottom is probably more useful. But in general, it's more "correct" to have the roots on top. There's no particular reason for this, but a lot of teachers want it like that.

But, if you want to flip it's position, you will almost always have to conjugate.

Answer 9

Thanks and God bless

Answer 10

You're welcome.