E-StoreHome » Ask & Discuss » Mathematics. » Algebra « Back to Discussion
Algebra
statement-1: the function f(x)=x^2 e^-x^2 sin lxl is evenstatement-2: product of two odd functions is an even function(1) statement 1 is true,statement 2 is true, statement 2 is not a correct explanation for statement 1(2) statement 1 is true,statement 2 is true, statement 2 is a correct explanation for statement 1
Comments (9)
f(x)=x^2 e^-x^2 sin lxl
f(-x)=(-x)^2 e^-(-x)^2 sin l-xl => x^2 e^-x^2 sin lxl
therefore f(x) = f(-x)
therefore even function
x^2 e^-x^2 sin lxl= x.(x e^-x^2 sin lxl)
since x is odd and x e^-x^2 sin lxl is also odd
but there product is a even function
hence ans is (2)
Ofcourse, Varun.
Consider 2 odd functions f(x) and g(x).
Hence, f(-x) = - f(x) and g(-x) = - g(x)
f(-x)g(-x) = f(x)g(x) which makes their product an even function.
Thought of the day: Cloud nine gets all the publicity, but cloud eight actually is cheaper, less crowded, and has a better view.
Preparing for IIT-JEE ?
Arihant Revision Package for IIT JEE - Books, Practice Tests + Rank Predictor
@ INR 1,995/-
For Quick Info
Find Posts by Topics
Physics.
TopicsMathematics.
Chemistry.
Biology
Institutes
Parents
Board
Fun Zone
|
|
|
|
|
| 35,229,755 Engineering Questions Attempted |
6,69,530 Visitors Monthly |
79 Engg. Exam Covered |
1979 Students Currently Online |
Connect with Us  |
 |
Its a tricky one so I'm not sure if I'll end up with the correct answer.
Obviously, both the statements are correct. And at first glance, we dont see any significant relation between the two statements.
Just for the sake of it, rewrite f(x) = x^2 e^-x^2 sin lxl as f(x) = x.(x e^-x^2 sin lxl) ..
So, we have two odd functions now. And hence statement 2 is the correct explanation of statement 1.
My answer, (2).