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This question asks us to determine of the given function is even order. Neither we know we have. Why is X cubed over X squared minus what? Because we know that a negative value of X will change the sign. We know it changes the sound of the numerator, but not the denominator. Therefore, in this context of function will indeed change signs indicating that it is odd.
So we have the functions. I love eggs. Is he good? X cubed minus X To find out if dysfunction is odd, even neither we need to find out what of negative X is equal to. So we have negative X cubed minus negative X Would you single too? Negative X cubed plus x recall that this right here It's also equal to negative of axe because negative off of axes you couldn't get executed plus X So we see that this right here is you got to this therefore you just determined that half of negative x the secret to negative Kovacs making f of X nod function.
If we look at of X is equal to X cubed plus X, you can start so to figure out if the the function is even auto neither what we need to find is what f of negative X equal to So here we have negative execute. Plus no your ex, which is equal to negative X cubed minus x So we know that of actors you goto execute plus x so negative half of axe Is he good to negative X cubed minus X So you just term IND that f of negative axe Is he good the negative f of X? Because this was the same as this right here, which means that this function right here is odd.