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  • - [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.

- [Instructor] We are told Jayden was asked to determine

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A2 初級

偶數和奇數函數。代數2|代數2|Khan Academy (Even and odd functions: Find the mistake | Transformations of functions | Algebra 2 | Khan Academy)

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    林宜悉 發佈於 2021 年 01 月 14 日
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