Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = \frac { - x ^ { 3 } } { 9 x ^ { 2 } + 7 }$$
A) even
B) odd
C) neither

Question

Quizplus · Accepted Answer

To determine if the function is even, odd, or neither, we substitute $-x$ for $x$ and simplify. For the given function $f(x) = \frac{-x^3}{9x^2 + 7}$, substituting $-x$ gives $f(-x) = \frac{-(-x)^3}{9(-x)^2 + 7} = \frac{x^3}{9x^2 + 7}$. This is the negative of the original function, $f(-x) = -f(x)$, which means the function is odd.

Determine Algebraically Whether the Function Is Even, Odd, or Neither f(x)=−x39x2+7f ( x ) = \frac { - x ^ { 3 } } { 9 x ^ { 2 } + 7 }f(x)=9x2+7−x3​

Determine Algebraically Whether the Function Is Even, Odd, or Neither $f ( x ) = \frac { - x ^ { 3 } } { 9 x ^ { 2 } + 7 }$