Given f(x)=cos c and g(x)=cot x, what are the domain and range of f(g(x))?
1 answer:
Answer:
Alternative C is the correct answer
Step-by-step explanation:
The first step is to determine the composite function;
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;
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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You can solve this analytically to get
.. 55000*(1 +x/100)^10 = 108193
.. (1 +x/100)^10 = 108193/55000
.. 1 +x/100 = (108193/55000)^(1/10)
.. x = 100*((108193/55000)^(1/10) -1) ≈ 7.00
but I find it just as fast to have a graphing calculator do it.
The city's population is increasing 7% per year.
.. 55000*(1 +x/100)^10 = 108193
.. (1 +x/100)^10 = 108193/55000
.. 1 +x/100 = (108193/55000)^(1/10)
.. x = 100*((108193/55000)^(1/10) -1) ≈ 7.00
but I find it just as fast to have a graphing calculator do it.
The city's population is increasing 7% per year.