1. 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.

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

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

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