# Operations of square root functions

• Oct 17th 2009, 01:15 PM
sharpiemarker
Operations of square root functions
I can't remember square root rules and I'm looking for

f+g, f-g, fxg, f/g

f(x)=sqrt(1+x)
g(x)=sqrt(1-x)
• Oct 17th 2009, 01:22 PM
Matt Westwood
Quote:

Originally Posted by sharpiemarker
I can't remember square root rules and I'm looking for

f+g, f-g, fxg, f/g

f(x)=sqrt(1+x)
g(x)=sqrt(1-x)

There are no simple rules for adding / subtracting square roots, but you do have:

$\sqrt a \sqrt b = \sqrt {ab}, \frac {\sqrt a} {\sqrt b} = \sqrt {\frac a b}$. That may help a little.
• Oct 17th 2009, 01:25 PM
sharpiemarker
Quote:

Originally Posted by Matt Westwood
There are no simple rules for adding / subtracting square roots, but you do have:

$\sqrt a \sqrt b = \sqrt {ab}, \frac {\sqrt a} {\sqrt b} = \sqrt {\frac a b}$. That may help a little.

That does help. Any suggestions for the addition and subtraction of the functions? Thanks!
• Oct 17th 2009, 01:30 PM
Matt Westwood
Quote:

Originally Posted by sharpiemarker
That does help. Any suggestions for the addition and subtraction of the functions? Thanks!

(shrug) $f(x) + g(x) = \sqrt{1+x} + \sqrt{1-x}$ and similar for the subtract one is probably as best as you can do.

Unless there's something embarrassingly basic that I've completely forgotten.
• Oct 17th 2009, 01:35 PM
sharpiemarker
Quote:

Originally Posted by Matt Westwood
(shrug) $f(x) + g(x) = \sqrt{1+x} + \sqrt{1-x}$ and similar for the subtract one is probably as best as you can do.

Unless there's something embarrassingly basic that I've completely forgotten.

Hehe, I see we're on the same page then. It seems like I should simplify that but I'm not seeing how. Thanks for the suggestions.
• Oct 17th 2009, 02:19 PM
mr fantastic
Quote:

Originally Posted by sharpiemarker
Hehe, I see we're on the same page then. It seems like I should simplify that but I'm not seeing how. Thanks for the suggestions.

It does not simplify any further (Matt was joking - he's forgotten nothing).