f(x) = cot(2 arccos x)
I have only had one class so far and this is due in a bit, I am not sure what to do?
So far I used identities and simplified into
f(x) = ((cos/sin)(arccos/1)-1)/(2(cos/sin)(arccos))
f(x) = (1-sinx)/2 ??
I still have no conception of if this is right or even if I'm doing the right thing. Just some slight hints or explanations of the broad concept would be fantastic
First, Otis gave you the very broad brush picture for such problems.
You have a composite function
f(x)=g(h(x)).
What is the domain of h? Wherever h(x) is undefined, then f(x) will be undefined. Make sense?
What is h(x) in this problem? What is its domain? What is its range?
Now g may have a very broad domain, but not all of that domain may be relevant to the composite function. First, we are limited to the domain of h. Let h(x) = y. What is the range on y? Nothing outside that range is relevant to g(h(x)) = g(y). In other words, the range of h is going to limit the domain of g with
respect to the composite function. Furthermore, any value in the range of h that is not in the domain of g is also not in the domain of the composite function. So we must ask what is the domain of g within the limits set by the range of h?
What is g(y) in this problem? What are the limits within which we must look for a domain?
Second, I presume you are working with radian measure. Is that correct?
Third, I do not see a necessity to transform the cotangent, but if you do so, you need to do so correctly.
f(x)=cot(2∗arccos(x))=sin{2∗arccos(x)}cos{2∗arccos(x)}