Question

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

Answer choices:

A. Domain: All real numbers; Range: all real numbers.

B. Domain: All real numbers x except x does not equal npi for all integers n; Range: all real numbers.

C. Domain: All real numbers x except x does not equal npi for all integers n; Range: -1 is less than or equal to y is less than or equal to 1.

D. Domain: All real numbers; Range: -1 is less than or equal to y is less than or equal to 1.

Answer 1

Alternative C is the correct answer

Explanation:

The first step is to determine the composite function;

`f[g(x)]`

`f[g(x)]=cos[cot(x)]`

We then employ a graphing utility to determine the range and the domain of the new function.

The range is the set of y-values for which the function is defined. In this case it is;

`[-1,1]`

On the other hand, the domain refers to the set of the x-values for which the function is real and defined. In this case; it is the set of real numbers x except x does not equal npi for all integers n.