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Current time:0:00Total duration:3:56

CCSS.Math:

we are asked are the following functions even odd or neither so pause this video and try to work that out on your own before we work through it together all right now let's just remind ourselves of a definition for even and odd functions one way to think about it is what happens when you take F of negative x if F of negative x is equal to the function again then we're dealing with an even function if we evaluate F of negative x instead of getting the function we get the negative of the function then we're dealing with an odd function and if neither of these are true it is neither so let's go to this first one right over here f of X is equal to 5 over 3 minus X to the fourth and the best way I can think about tackling this is let's just evaluate what F of negative x would be equal to that would be equal to 5 over 3 minus and everywhere we see an X we're going to replace that with a negative x to the 4th power now what is negative X to the fourth power well if you multiply a negative times a negative times a negative how many times did I do that if you if you take a negative to the fourth power you're going to get a positive so that's going to be equal to 5 over 3 minus X to the 4th which is once again equal to f of X and so this first one right over here F of negative x is equal to f of X it is clearly even let's do another example so this one right over here G of X let's just evaluate G of negative x and at any point you feel inspired and you didn't figure it out the first time pause the video get and try to work it out on your own well G of negative x is equal to 1 over negative x plus the cube root of negative x and see let's see can we simplify this any well we could rewrite this as the negative of 1 over X and then I could view negative x as the same thing as negative 1 times X and so we can factor out or I should say we could take the negative 1 out of the radical what is the cube root of negative one well it's negative one so we could say - we could say minus one times the cube root or we could just say the negative of the cube root of x and then we can factor out a negative so this is going to be equal to negative of one over X plus the cube root of x which is equal to the negative of G of X which is equal to the negative of G of X and so this is odd F of negative x is equal to the negative of f of X so in this case it's G of X G of negative x is equal to the negative of G of X let's do the third one so here we've got H of X and let's just evaluate H of negative x H of negative X is equal to two to the negative X plus two to the negative of negative X which would be two to the positive x well this is the same thing as our original H of X this is just equal to H of X you just swap these two terms and so this is clearly even and then last but not least we have J of X so let's evaluate J of I right all right why let's evaluate J of negative X is equal to negative x over 1 minus negative X which is equal to negative x over 1 plus X and let's see there's no clear way of factoring out a negative or doing something interesting where I get either back to J of X or I get to negative J of X so this one is neither and we're done