Question

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

Answer 1

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

Answer 2

my answer again is letter c i dont know y.

Answer 3

if a or b my answer the wiki is correct

Answer 4

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

The function in c is not odd ...

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

odd x odd = even

even x odd= odd

even x even= even

Answer 9

yun!

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

OMG its LETTER B because cos x is an even function

Answer 15

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

Answer 16

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).

Answer 17

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.

Answer 18

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

Answer 19

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)

Answer 20

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

Answer 21

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