anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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JamesJ
  • JamesJ
Test and see. What's the definition of an odd function?
anonymous
  • anonymous
my answer again is letter c i dont know y.
anonymous
  • anonymous
if a or b my answer the wiki is correct

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More answers

JamesJ
  • JamesJ
By definition, a function f is odd if \[ f(-x) = -f(x) \] The function in c is not odd ...
anonymous
  • 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
anonymous
  • 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
JamesJ
  • JamesJ
...because \[ \cos(-x) = \cos(x) \] hence \[ e^{\cos(-x) } = e^{\cos(x)} \]
anonymous
  • anonymous
odd x odd = even even x odd= odd even x even= even
anonymous
  • anonymous
yun!
anonymous
  • 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
JamesJ
  • JamesJ
No. The function is D is not odd, because \[ \sin^2(-x) = (\sin(-x))^2 = (-\sin x)^2 = \sin^2 x \]
JamesJ
  • JamesJ
hence the function in D and C are both even functions: \[ f(-x) = f(x) \]
anonymous
  • anonymous
how could i know a and b are odd? i feel sinx and cosx are the same
anonymous
  • anonymous
OMG its LETTER B because cos x is an even function
JamesJ
  • JamesJ
No. Try and work it out by explicitly evaluating expressions.
anonymous
  • 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).
JamesJ
  • 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.
anonymous
  • anonymous
f(x) = -sinx is odd function so f(x) = xcosx
JamesJ
  • 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)
anonymous
  • anonymous
its like -f(x) = f(-x) thank your mister james
JamesJ
  • JamesJ
By definition, a function f(x) is odd if f(-x) = -f(x)

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