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 Dimetri? Explain why or why not.

Question

Mathematics

Riley Stephenson

9 January, 08:19

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 Dimetri? Explain why or why not.

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Answers (1)

Know the Answer?

Chance Calhoun · Answer 1

No, I do not.

Explanation:

Algebraically, an odd function is one where f (-x) = - f (x). This means that if we substitute - x for every x in the function, it should be the same as switching every sign in the function. This does not always work.

For example, if f (x) = x ³ + 7:

f (-x) = (-x) ³ + 7=-x ³ + 7.

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