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## Symmetry of functions

Current time:0:00Total duration:3:35

# Even and odd functions: Find the mistake

CCSS Math: HSF.BF.B.3

## Video transcript

- [Instructor] We are told
Jayden was asked to determine whether f of x is equal to
x minus the cube root of x is even, odd, or neither. Here is his work. Is Jayden's work correct? If not, what is the first step
where Jayden made a mistake? So pause this video and
review Jayden's work, and see if it's correct, or if it's not correct tell
me where it's not correct. All right, now let's work this together. So, let's see, just to remind ourselves what Jayden's trying to
do, he's trying to decide, whether f of x is even, odd, or neither. And f of x is expressed, or is defined, as x minus the cube root of x. So let's see, the first
thing that Jayden did is he's trying to figure out
what is f of negative x? Because remember, if f of negative x is equal to f of x, we are even, and if f of negative x is equal to negative f
of x, then we are odd. So it makes sense for him to find the expression
for f of negative x. So he tries to evaluate f of negative x, and when he does that, everywhere where he sees an x in f of x, he replaces it with a negative x. So that seems good. And then, let's see, this
becomes a negative x, that makes sense, minus, and then, a negative x under the radical, and this is a cube root right over here, that's the same thing
as negative one times x. The cube root of negative
one is negative one. So he takes that negative
out of the radical, out of the cube root. So this makes sense, and
so then he has a negative x and you subtract a negative,
you get a positive. So then that makes sense. And then, the next thing he
says is, or he's trying to do, is check if f of negative x is equal to f of x or f of negative x. So he's gonna check whether
this is equal to one of them. And so here Jayden says, negative
x plus the cube root of x, so that's what f of negative
x, what he evaluated it to be, isn't the same as f of x, now
let's see is that the case? Is it not the same as f of x? Yup it's definitely, it's
not the same as f of x, or negative f of x which is equal to negative x minus the cube root of x. Now that seems a little bit fishy. Did he do the right
thing, right over here? Is negative f of x equal to negative x minus the cube root of x? Let's see, negative of f of x is going to be a negative
times this entire expression, it's going to be a negative up front, times x minus the cube root of x, and so this is going to be equal to, you distribute the negative sign, you get negative x plus
the cube root of x. So Jayden calculated the wrong negative f of x right over here. So, he isn't right that negative
x plus the cube root of x, it is actually the same
as negative f of x. So he's wrong right over here. So Jayden's mistake is right
over here, really it looks like he didn't evaluate
negative f of x correctly. So Jayden's work, is
Jayden's work correct? No. If not, what is the first step
where Jayden made a mistake? Well it would be step two. What he should have said is, it actually is the same
as negative f of x, and so therefore his conclusion should be that f of x is odd.