1. ## Finding the Domain

Let f(x)=sinx, g(x)=sqrt(1-x^2). Find (fog)(x) and (gof)(x) and their domain.

Well I can answer (fog)(x) and (gof)(x), which are sin[sqrt(1-x^2)], and [sqrt(1-sinx^2)] respectively. However, I dont know how to find the domain. Any help would be appreciated. Thanks

2. Originally Posted by johntuan
Let f(x)=sinx, g(x)=sqrt(1-x^2). Find (fog)(x) and (gof)(x) and their domain.

Well I can answer (fog)(x) and (gof)(x), which are sin[sqrt(1-x^2)], and [sqrt(1-sinx^2)] respectively. However, I dont know how to find the domain. Any help would be appreciated. Thanks
write $(\sin x )^2$ or $\sin^2 x$. $\sin x^2 = \sin (x^2)$ is different.

anyway, the domain is the set of input values (x-values in this case) for which a function is defined. you need to find the x-values that work therefore.

for the square root function, the thing being square rooted has to be greater than or equal to zero for the function to work. the sine function works for all real values of x

can you figure out the domains now?

3. for f o g...would the domain be -1<x<1
and im not too sure for g o f..because of the sin function

4. Originally Posted by johntuan
for f o g...would the domain be -1<x<1
yes

and im not too sure for g o f..because of the sin function
the same principle applies. you want $1 - \sin^2 x \ge 0$. this happens to always be the case, so that the domain is all $x \in (- \infty, \infty)$