# functions and domains

• Aug 31st 2008, 08:48 PM
sjenkins
functions and domains
Let f(x)=square root (1+x) and g(x)=square root (1-x) Find f+g, f-g, fg, f/g and their domains.

I know that to add these functions, I have to add sqrt (1+x) and sqrt (1-x) but I'm unclear how to add square roots and I'm not sure how to find the domains.
• Aug 31st 2008, 09:07 PM
ThePerfectHacker
Quote:

Originally Posted by sjenkins
Let f(x)=square root (1+x) and g(x)=square root (1-x) Find f+g, f-g, fg, f/g and their domains.

I know that to add these functions, I have to add sqrt (1+x) and sqrt (1-x) but I'm unclear how to add square roots and I'm not sure how to find the domains.

Domain of $\displaystyle \sqrt{1+x}$ is $\displaystyle x\geq -1$.
Domain of $\displaystyle \sqrt{1-x}$ is $\displaystyle x\leq 1$.

Thus, domain of $\displaystyle f+g,f-g,fg$ is die intersection i.e. $\displaystyle -1\leq x\leq 1$

While domain of $\displaystyle f/g$ is $\displaystyle -1\leq x\leq 1$ minus $\displaystyle 1$ since denominator is zero.
This gives us $\displaystyle -1\leq x <1$.