To the negative of f of x, or in this case it's g of x, g of negative x is equal

And so this is odd, f of negative x is 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. Negative of the cube root of x and then we can factor out a negative, so this is going to be equal One times the cube root or we could just say the What is the cube root of negative one? Well it's negative one, so we could say minus Take the negative one out of the radical. Well g of negative x isĮqual to one over negative x plus the cube root of negative x and let's see, can we simplify this any? Well we could rewrite thisĪs the negative of one over x and then yeah, I could view negative x as the same thing as negative one times x and so we can factor out, or I should say we could It out the first time, pause the video again and try 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 Is once again equal to f of x and so this first one right over here, f of negative x is equal toį of x, it is clearly even. To the fourth power, you're going to get a positive, so that's going to beĮqual to five over three minus x to the fourth, which Many times did I do that? If you take a negative Negative times a negative times a negative, how X to the fourth power? Well if you multiply a That with a negative x, to the fourth power. That would be equal toįive over three minus and everywhere we see an x, we're gonna replace Think about tackling this is let's just evaluate what f of negative x would be equal to. Three minus x to the fourth, and the best way I can One right over here, f of x is equal to five over And if neither of theseĪre true it is neither.

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. To the function again, then we're dealing with an even function. One way to think about it is what happens when you take f of negative x? If f of negative x is equal

All right, now let's just remind ourselves of a definition forĮven and odd functions. To work that out on your own before we work through it together. We are asked are the following functionsĮven, odd, or neither? So pause this video and try

Is 3x4 2x 5 even or odd