ISRO 2006-ECE Functions

Question

$x^3$ + $x$ sin $x$ is

a) Constant function

b) Odd function

c) Even function

d) Periodic function

Answer 1

As the given function is not periodic because of x^3 part and also by refering to the link  https://www.desmos.com/calculator/cwpyyqjjmx we do not get any periodicity in the resultant graph.

For Even function F(-x) = F(x)

For Odd function F(-x) = -F(x)

Replacing x with -x in above function we get -(x^3) + x sin(x) which  is neither even nor odd

The above function is  Constant because it does involve constant term when we place the value of x then a constant will be there in the form of x^3 along with x sin(x)

Hence it will be Constant function

So option A is Correct.

Comments

but function has also x^3 term

---

@akriti you are right even if we had xsinx still it is not periodic. Should be none of these

---

because of this term also function is showing constant behaviour