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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

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