Answer
384k+ views
Hint: For checking whether a function is one-one or not, we need to check its graph. If we draw a horizontal line on the graph, which cuts it at more than one point, then we say that the function is not one—one. But if every possible horizontal line cuts the graph at most one point, then we say that the function is a one-to-one function.
Complete step-by-step solution:
According to the question, the function is
$f\left( x \right) = 3\sin 2x + 5$
Considering the graph of the above function, we have
Now, we know that a one-to-one function is a function in which every value of the co domain is the image of at most one value of the domain. This means that every horizontal line drawn on the graph of a one-to-one function to intersect it, will cut it at most on point. So we draw a horizontal line, say
$y = 5$, on the above graph so that we get
As we can see that the horizontal line $y = 5$ is cutting the graph at multiple points. So we can say that the given function is not a one-to-one function.
Now, we know that a function is invertible if and only if it is injective as well as subjective, that is, it is one-to-one as well as onto. But since we have shown above that the given function is not one-to-one, so it is not invertible.
Hence, the inverse of the given function does not exist.
Note:
We should keep in mind that the inverse of a function does not mean to simply express x in terms of y. The inverse of a function is itself a function and so it must follow all the properties of a function. Hence, for a function to be invertible, firstly it must be one-to-one as well as onto. The inverse of a function will only exist if it is a one-one function.
Complete step-by-step solution:
According to the question, the function is
$f\left( x \right) = 3\sin 2x + 5$
Considering the graph of the above function, we have
![seo images](https://www.vedantu.com/question-sets/c81d792f-21f2-43d2-b1fb-2ecadec3f8bd7945832851163157403.png)
Now, we know that a one-to-one function is a function in which every value of the co domain is the image of at most one value of the domain. This means that every horizontal line drawn on the graph of a one-to-one function to intersect it, will cut it at most on point. So we draw a horizontal line, say
$y = 5$, on the above graph so that we get
![seo images](https://www.vedantu.com/question-sets/15a69058-45b0-4b90-8ddf-305938a4c3fa766014461793718678.png)
As we can see that the horizontal line $y = 5$ is cutting the graph at multiple points. So we can say that the given function is not a one-to-one function.
Now, we know that a function is invertible if and only if it is injective as well as subjective, that is, it is one-to-one as well as onto. But since we have shown above that the given function is not one-to-one, so it is not invertible.
Hence, the inverse of the given function does not exist.
Note:
We should keep in mind that the inverse of a function does not mean to simply express x in terms of y. The inverse of a function is itself a function and so it must follow all the properties of a function. Hence, for a function to be invertible, firstly it must be one-to-one as well as onto. The inverse of a function will only exist if it is a one-one function.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)