Question

Given f(x) = cos x and g(x) = cotx, what are the domain and range of f(g(x))

Answer 1

Given the following function:

`f(x)=cos(x);g(x)=cot(x)`

We will write the composite function f(g(x))

So, the composite function will be as follows:

`f(g(x))=cos(cot\text{ }x)`

The domina of the composite function is the domain of the cosine function except for the values of the x which is undefined for cot (x)

So, the domain will be:

Domain = All real numbers except for x≠ nπ

The range of the composite function is the range of the cosine function

Range = [-1, 1]

So, the answer will be option C