Answer
424.2k+ views
Hint: Degree of the function can be defined as the highest power of the degree of the variable. In other words it is the sum of the raised power of the parameters involved in a function. For example, the degree of the function $f(x) = 2x + 9$ is 1 as the highest power of the variable here is 1 while the degree of the function $g(x) = xy + {x^2}y$ is 3 which comes by adding the power of the parameters which are in multiplication with each other. In this question, two functions have been given for which the degree of the product of the two functions needed to be determined. We need to first multiply the terms of the functions in the variable $x$ and then, evaluate the degree of the resultant function.
Complete step by step solution: Substitute $A = (3x + 6){\text{ and }}B = (2{x^2} + 3x + 4)$ in the function AB we get,
$
AB = (3x + 6)(2{x^2} + 3x + 4) \\
= 6{x^3} + 9{x^2} + 12x + 12{x^2} + 18x + 24 \\
= 6{x^3} + 21{x^2} + 30x + 24 \\
$
From the above equation, we can see that the highest power of the variable $x$ is 3.
Hence, the degree of the function AB is 3 where $A = (3x + 6){\text{ and }}B = (2{x^2} + 3x + 4)$.
Option B is correct.
Note: Alternatively, this question can also be solved by adding the degree of the equation $A = (3x + 6){\text{ and }}B = (2{x^2} + 3x + 4)$ as the resultant equation is the product of the two functions. Degree of the individual functions should only be added if the resultant function is in the product form of the two individual functions.
Complete step by step solution: Substitute $A = (3x + 6){\text{ and }}B = (2{x^2} + 3x + 4)$ in the function AB we get,
$
AB = (3x + 6)(2{x^2} + 3x + 4) \\
= 6{x^3} + 9{x^2} + 12x + 12{x^2} + 18x + 24 \\
= 6{x^3} + 21{x^2} + 30x + 24 \\
$
From the above equation, we can see that the highest power of the variable $x$ is 3.
Hence, the degree of the function AB is 3 where $A = (3x + 6){\text{ and }}B = (2{x^2} + 3x + 4)$.
Option B is correct.
Note: Alternatively, this question can also be solved by adding the degree of the equation $A = (3x + 6){\text{ and }}B = (2{x^2} + 3x + 4)$ as the resultant equation is the product of the two functions. Degree of the individual functions should only be added if the resultant function is in the product form of the two individual functions.
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)