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## anonymous 4 years ago which of the following is an odd function? a. f(x)= xcosx b.f(x)= xsinx c.f(x)= e ^cosx d.f(x)=sin^2x

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1. JamesJ

Test and see. What's the definition of an odd function?

2. anonymous

my answer again is letter c i dont know y.

3. anonymous

if a or b my answer the wiki is correct

4. JamesJ

By definition, a function f is odd if $f(-x) = -f(x)$ The function in c is not odd ...

5. anonymous

you need to check to see if $f(-x)=f(x)$ for even or if $f(-x)=-f(x)$ for odd and there is no shame in trying it with numbers if the x's get confusing

6. anonymous

it won't be a proof, but it will give you an idea of what is going on. then you can do it with a variable

7. JamesJ

...because $\cos(-x) = \cos(x)$ hence $e^{\cos(-x) } = e^{\cos(x)}$

8. anonymous

odd x odd = even even x odd= odd even x even= even

9. anonymous

yun!

10. anonymous

ic all your answer is correct but a or b are the same right? i only need to choose 1 letter and it is letter D

11. JamesJ

No. The function is D is not odd, because $\sin^2(-x) = (\sin(-x))^2 = (-\sin x)^2 = \sin^2 x$

12. JamesJ

hence the function in D and C are both even functions: $f(-x) = f(x)$

13. anonymous

how could i know a and b are odd? i feel sinx and cosx are the same

14. anonymous

OMG its LETTER B because cos x is an even function

15. JamesJ

No. Try and work it out by explicitly evaluating expressions.

16. anonymous

Geometrically, the graph of an odd function has rotational symmetry with respect to the origin, meaning that its graph remains unchanged after rotation of 180 degrees about the origin. Examples of odd functions are x, x3, sin(x), sinh(x), and erf(x).

17. JamesJ

Yes. But stop avoiding doing the calculation. Take each of the functions in turn and evaluate f(-x). See if it equal to -f(x) or not. If it is, then f(x) is odd. That is how you answer this question.

18. anonymous

f(x) = -sinx is odd function so f(x) = xcosx

19. JamesJ

f(x) = x.cos(x) is an odd function yes. Why? Because f(-x) = (-x).cos(-x) = -x.cos(x) , because cos(-x) = cos(x) = -f(x)

20. anonymous

its like -f(x) = f(-x) thank your mister james

21. JamesJ

By definition, a function f(x) is odd if f(-x) = -f(x)

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