Determine if the function is even, odd, or neither.
-$$f ( x ) = \frac { 5 } { x + 9 }$$
A) Even
B) Odd
C) Neither

Question

Quizplus · Accepted Answer

To check evenness, we substitute -x for x and simplify:

$f(-x) = \frac{5}{-x+9} = \frac{-5}{x-9}$

To check oddness, we need to check if $f(-x)=-f(x)$ for all x:

$-\frac{5}{x+9} = -\frac{5}{x+9}$

This is true for all x, so the function is odd. However, we only needed to find one disagreement to show it is not odd. Since it is not odd, the function is neither even nor odd.

Determine If the Function Is Even, Odd, or Neither f(x)=5x+9f ( x ) = \frac { 5 } { x + 9 }f(x)=x+95​

Determine If the Function Is Even, Odd, or Neither $f ( x ) = \frac { 5 } { x + 9 }$