Determine whether the given function is even, odd, or neither.
-$$f ( x ) = x ^ { 5 } - x ^ { 4 }$$
A) Neither
B) Even
C) Odd

Name: Determine whether the given function is even, odd, or neither. -\[f ( x ) = x ^ { 5 } - x ^ { 4 }\] A) Neither B) Even C) Odd
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Question

Quizplus · Accepted Answer

A function is even if $ f(x) = f(-x) $ and odd if $ f(-x) = -f(x) $. For $ f(x) = x^5 - x^4 $, $ f(-x) = (-x)^5 - (-x)^4 = -x^5 - x^4 $, which is neither equal to $ f(x) $ nor $-f(x)$. Thus, the function is neither even nor odd.

Determine Whether the Given Function Is Even, Odd, or Neither f(x)=x5−x4f ( x ) = x ^ { 5 } - x ^ { 4 }f(x)=x5−x4

Determine Whether the Given Function Is Even, Odd, or Neither $f ( x ) = x ^ { 5 } - x ^ { 4 }$