Question

The domain of the function \[f\left( x \right) = \sin \dfrac{1}{x}\] is
A. \[R\]
B. \[{R^ + }\]
C. \[R - \left\{ 0 \right\}\]
D. \[{R^ - }\]

Answer 1

Hint: In the given question, we have been asked the domain of given trigonometric function. To determine the domain, we just check what values the argument of the function can have. We subtract the values or the range of the values which cannot be substituted into the argument.

Complete step-by-step answer:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set
The given function is \[f\left( x \right) = \sin \dfrac{1}{x}\] .
For finding the domain, we just consider the argument, which is \[\dfrac{1}{x}\] .
Clearly, \[\dfrac{1}{x}\] can take any value as input except for \[0\] , as this is going to give us \[\dfrac{1}{0}\] , which is an indeterminate form.
Hence, the domain is \[R - \left\{ 0 \right\}\] .
So, the correct answer is “Option C”.

Note: So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we think about the concept or formula which contains the known and the unknown and pick the one which is the most suitable and the most effective for finding the answer of the given question. Then we use the results or finding of the concept and apply it to our question. It is really important to know and follow all the results of the concepts if we have to solve the question correctly, as one slightest error gives the incorrect result.