
The period of the function equal to
A)
B) C) D)
Answer
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Hint: To solve this problem we need to have knowledge about functions concept. We know that the period of any function which is in the form h(x) +g(x) is the L.C.M of the periodic function h(x) and g(x).
Complete step-by-step answer:
Given function is
We know that period of is
If we observe the terms in the given function they are in the form which is a composite function.
We know that the period of a function of type is the same as the period of g(x).
Now by using the above concept we can say that period of is and the period of is also . Since period of is .
Here the given function f(x) is of the form .
We know that if any function is of the form then the period of that function will be the L.C.M of periodic function of p(x) and q(x).
From the given function f(x) we can say that whose period is and whose period also .
Therefore by applying the above condition to the given function we can say that L.C.M of .
Hence the period of the function is .
So, Option (D) is the correct answer.
Note: In this type of problems we won’t observe the given function clearly and directly apply the condition to get the period of the function which is a very wrong process. Here in the given question the function f(x) has one more function in the term of function. So here before finding the period of the function f(x) we have to find the period of the innermost function. In this case the innermost function is a composite function.
We can observe the period of individual functions in the below graphs.
Graph of
Graph of
Graph of
Graph of
Graph of
Complete step-by-step answer:
Given function is
We know that period of
If we observe the terms in the given function they are in the form
We know that the period of a function of type
Now by using the above concept we can say that period of
Here the given function f(x) is of the form
We know that if any function is of the form
From the given function f(x) we can say that
Therefore by applying the above condition to the given function we can say that L.C.M of
Hence the period of the function
So, Option (D) is the correct answer.
Note: In this type of problems we won’t observe the given function clearly and directly apply the condition to get the period of the function which is a very wrong process. Here in the given question the function f(x) has one more function in the term of function. So here before finding the period of the function f(x) we have to find the period of the innermost function. In this case the innermost function is a composite function.
We can observe the period of individual functions in the below graphs.
Graph of

Graph of

Graph of

Graph of

Graph of

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