Question

Let g(x)= 1/(sqr(x-6)) . Evaluate the expression (g(x)- g(10))/(x-10) and then simplify the result.

*sqr= square root

Answer 1

what is g(10)?

Answer 2

It;s just g(10). I think the whole expression is for limits, but I can't figure out how to do this.

Answer 3

\[g(x) = \frac{1}{\sqrt{x-6}}\\g(10) = \frac{1}{\sqrt{10-6}}=\frac{1}{2}\]you need
\[\frac{g(x)-g(10)}{x-10}=\frac{\frac{1}{\sqrt{x-6}}-\frac{1}{2}}{x-10}=\frac{\frac{2-\sqrt{x-6}}{2(x-6)}}{x-10}=\frac{2-\sqrt{x-6}}{2(x-10)(x-6)}\]

Answer 4

im not sure what you want to do here...

Answer 5

You just need to simplify it. And how did you get (x-6)? Wouldn't it still be \[\sqrt{x-6}\]?
Not only do we both have different answers, but both are not one of the MC answers.

Answer 6

yes it should be sqrt sorry. i hate latex...
\[\frac{2-\sqrt{x-6}}{2\sqrt{x-6}(x-10)}\]

Answer 7

Nevermind I got the right answer now! I just had to multiply everything out by \[\sqrt{x-6}\] so that the bottom would no longer be radical :p!