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.

the image of (6, 9) under a dilation is (4, 6). the scale factor is

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.