Answer to Question #132375 in Calculus for marcus

Question

Determine if the following function is even, odd, or neither.

f(x) = -9x4 + 5x + 3

Answer 1

ANSWER

$f(x) = -9x^4 + 5x + 3$ is neither even nor odd.

SOLUTION

$f(x) = -9x^4 + 5x + 3$

$f(-x) = -9(-x)^4 + 5(-x) + 3$

$= -9x^4 - 5x + 3$

$-f(x) = - (-9x^4 + 5x + 3)$

$= 9x^4 - 5x - 3$

$f(x)$ is even if and only if $f(x) = f(-x)$

$Now, \space f(x) \neq f(-x),$

$\space \therefore \space f(x) \space is \space not \space even$

$Also,$ $f(x)$ is odd if and only if $f(-x) = -f(x)$

$Now, \space f(-x) \neq -f(x),$

$\space \therefore \space f(x) \space is \space not \space odd$

Therefore, $f(x)$ is neither an even nor an odd function.