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

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.

Option C

Step-by-step explanation:

We know that the function has as its domain all real numbers, and as a range

 We know that the function

The denominator of the function can not be equal to 0. But for all where n is an integer number.

Therefore the domain of cot(x) are all real numbers except

The range of cot(x) are all real numbers

Then, the domain of f(g(x)) is:

x ∈ Domain g and g(x) ∈ Domain of f

Where:

Domain of g: All reals except

Domain of f: All reals.

This is:

Domain of f(g(x)):

All real numbers except

Range of f(g(x)):

Therefore the correct option is:

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

ou would have 12 of each