Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = 4 x ^ { 5 } - 3 x ^ { 3 }$$
A) Neither
B) Odd
C) Even

Question

Quizplus · Accepted Answer

The function $f(x) = 4x^5 - 3x^3$ is odd because when we replace $x$ with $-x$, we get $f(-x) = 4(-x)^5 - 3(-x)^3 = -4x^5 + 3x^3 = -(4x^5 - 3x^3) = -f(x)$, which satisfies the definition of an odd function.

Determine Algebraically Whether the Function Is Even, Odd, or Neither f(x)=4x5−3x3f ( x ) = 4 x ^ { 5 } - 3 x ^ { 3 }f(x)=4x5−3x3

Determine Algebraically Whether the Function Is Even, Odd, or Neither $f ( x ) = 4 x ^ { 5 } - 3 x ^ { 3 }$