
Determine the domain and range of .
Answer
523.8k+ views
Hint: To solve this question, we will start by assuming . Also, while solving the question, we have to remember that a function always has one to one mapping, which means that one particular value of x will give a particular value of . Also, we should have some knowledge regarding .
Complete step-by-step answer:
In this question, we have been asked to find the domain and range of . For that, we will consider, . We know that such a type of function can also be written as . Now, according to the wave of , as shown in the figure below,
Complete step-by-step answer:
In this question, we have been asked to find the domain and range of
We can say that . So, we can say that after a period of time, value starts repeating. So, from the curve, we can see that if , then only we are getting all the different possible values of x, otherwise values are repeating. Therefore the range and domain of is and respectively.
Now, if we talk about , then we can say range and domain of the function will interchange because we are talking about inverse function here.
Hence, we can say that the range of can be given as and domain can be given as, .
Note: We can also solve this question from the graph of also, which looks like the figure below.
From the curve, we can say that the curve has one to one mapping for and values of goes from to , so the range is .
Now, if we talk about
Hence, we can say that the range of
Note: We can also solve this question from the graph of
From the curve, we can say that the curve has one to one mapping for
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