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**Unreal** Hi!

Determine whether the function is even, odd or neither.

1. $\displaystyle f(x) = x^3 \sin x$

The function is even since:

$\displaystyle f(-x) = -x^3\sin(-x) = x^3sinx$

The result of cubing a negative is negative and taking the sine of a negative gives a negative, and multiplying two negatives gives a positive.

Correct any flaws in this thinking process please!

2. $\displaystyle f(x) = \cos(\sinx)$

This function is even since:

$\displaystyle f(-x) = \cos(\sin(-x) = \cos(-\sin(x)) = -\cos(\sin(x) = \cos(\sinx)$