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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.

Respuesta :

Answer:

Alternative C is the correct answer

Step-by-step explanation:

The first step is to determine the composite function;

[tex]f[g(x)][/tex]

[tex]f[g(x)]=cos[cot(x)][/tex]

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;

[tex][-1,1][/tex]

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.

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