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cestrela7 [59]
3 years ago
9

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

Mathematics
1 answer:
Evgesh-ka [11]3 years ago
7 0

Answer:

Option C

Step-by-step explanation:

We know that the function y = cos(x) has as its domain all real numbers, and as a range -1\leq y\leq 1

 We know that the function cot(x) = \frac{cos(x)}{sin(x)}

The denominator of the function can not be equal to 0. But sin(x) = 0 for all x = n\pi where n is an integer number.

Therefore the domain of cot(x) are all real numbers except x = n\pi

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 x = n\pi

Domain of f: All reals.

This is:

Domain of f(g(x)):

All real numbers except n\pi

Range of f(g(x)):

 -1\leq y\leq 1

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.

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