dimetri says that a function that is made of terms where the variable is raised only to an odd power will be an odd function. do you agree with dimetr

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02-09-2022
Mathematics

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dimetri says that a function that is made of terms where the variable is raised only to an odd power will be an odd function. do you agree with dimetr

Sagot :

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tanvigupta426 tanvigupta426 · Answer 1 · 2022-09-13T09:59:07-04:00

The given function is not the odd function.

According to the statement

We have to find about the odd function.

So, For this purpose, we know that the

The odd function is that the function f is odd if the subsequent equation holds for all x and −x within the domain of f : −f(x)=f(−x) − f ( x ) = f ( − x ) Geometrically, the graph of an odd function has rotational symmetry with relevance the origin, meaning that its graph remains unchanged after a rotation of 180∘ about the origin.

From the given information:

dimetri says that a function that's fabricated from terms where the variable is raised only to an odd power are going to be an odd function

Then

Algebraically, an odd function is one where f(-x) = -f(x). this suggests that if we substitute -x for each x within the function, it should be the identical as switching every sign up the function. This doesn't always work.

For example, if f(x)=x³+7:

f(-x)=(-x)³+7=-x³+7.

However, since the 7 did not become -7, it is not the same as -f(x), so it is not an odd function.

So, The given function is not the odd function.

Learn more about odd function here

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