每次做啲數問我f(x)+1/f(x+1)/2f(x)係褪上定褪落定係乘大左都要let一次f(x)=x^2 plot 一次先知

:^(

:^(

:^(

What is the inverse function of a^x then?

巴打

:^(

中學未學inverse function㗎

:^(

y=a^x
x=a^y
log x = y log a
y = log a / log x?

y = log_a(x)

每次做啲數問我f(x)+1/f(x+1)/2f(x)係褪上定褪落定係乘大左都要let一次f(x)=x^2 plot 一次先知

:^(

:^(

:^(

What is the inverse function of a^x then?

巴打

:^(

中學未學inverse function㗎

:^(

Really?

We know that y=x is the mid-point locus between y=e^x and y=lnx

Locus同inverse function好似兩樣野嚟

:^(

Exponential function太perfect啦你個例子太特別
打個比喻我求其畫嘅一條locus佢可以冇inverse

Inverse一定有
只係inverse不一定係function

Try to invert y = e^(-x^2)

明白啲公式點嚟就唔難記

利申一下
我就已經明白咗
但我就諗唔到點解有啲人會唔明，點教都get唔到
我代入唔到佢地點諗

:^(

所以我先喺度問吓

自

:^(

我都唔明點解啲人唔明
明明家下中學數學書都有例題有applications
即使上堂老師講到成嚿屎都好
自己齋睇條式唔明 睇例題至少都唔會一頭霧水唔知教緊咩掛

:^(

:^(

你講下好， 如果要apply, 比如計physics d 數， 老師教得唔好自己睇example 都未必明到

Sor我答你唔到

:^(

中學純商加M1 依家u stat
見住條chapman-kolmogorov equation真心呢啲先叫難明

:^(

Btw physic書唔會講完條式就算 冇英文解釋做緊咩掛

:^(

係咪3007

:^(

:^(

:^(

唔係

:^(

明白啲公式點嚟就唔難記

個問題就係唔明點嚟

:^(

介唔介意具體講多少少?
或者舉啲例子，當中講吓你點樣唔明法?唔明邊一個位?

例如教個啲f(x)=2x+y+10 g(x)=2f(x) (當然會複雜啲)
睇老師做個陣 心諗啲xxyy做乜鳩搬嚟搬去有時唔見咗有時又出現番

:^(

有冇嘗試遂個step研究吓點解要咁樣郁?
如果你一下子就睇曬成個答案，好容易就會覺得全部係亂碼
但係如果你遂粒遂粒字去理解
當你理解曬每一步，再望多次成個步驟連答案，你就會get到佢up乜春

冇

:^(

我個數學老師間唔中會用screen show答案

:^(

連step都唔使寫 直接開電腦等幾分鐘就比我地抄

:^(

咁叫教書

:^(

我覺得真正教數學係要畀唔明嘅人睇到啲數係點樣郁法
例子：

:^(

仲要呢個老師教我高中三年

:^(

我諗住遲啲喺youtube睇hy啲片學下
希望dse有3甚至4

:^(

明明小學次次考試測驗都94分
上到中學F2開始連49分都可能冇

:^(

This is on9

We simply manipulate it by dividing both sides by 20

4x = 5y --> 4x/20=5y/20 --> x/5=y/4

每次做啲數問我f(x)+1/f(x+1)/2f(x)係褪上定褪落定係乘大左都要let一次f(x)=x^2 plot 一次先知

:^(

:^(

:^(

我理解唔到呢個

:^(

Btw function fx有equation就好易做

:^(

醒目

When x is replaced by x+1,
x_new +1 = x_old

So, new value of x is less than the original by 1
The graph is translated leftwards 1 unit.

大概係咁解

每次做啲數問我f(x)+1/f(x+1)/2f(x)係褪上定褪落定係乘大左都要let一次f(x)=x^2 plot 一次先知

:^(

:^(

:^(

What is the inverse function of a^x then?

巴打

:^(

中學未學inverse function㗎

:^(

Really?

We know that y=x is the mid-point locus between y=e^x and y=lnx

Locus同inverse function好似兩樣野嚟

:^(

Exponential function太perfect啦你個例子太特別
打個比喻我求其畫嘅一條locus佢可以冇inverse

Inverse一定有
只係inverse不一定係function

Try to invert y = e^(-x^2)

x = e^(-y^2)

仔細啲睇清楚人哋留言先啦好唔好

Original graph:

:^(

When inverted:

:^(

Something like this

每次做啲數問我f(x)+1/f(x+1)/2f(x)係褪上定褪落定係乘大左都要let一次f(x)=x^2 plot 一次先知

:^(

:^(

:^(

我理解唔到呢個

:^(

Btw function fx有equation就好易做

:^(

醒目

When x is replaced by x+1,
x_new +1 = x_old

So, new value of x is less than the original by 1
The graph is translated leftwards 1 unit.

大概係咁解

喔

:^(

明啦 我以為個/係除號
原來係講緊transformation

:^(

我理解方法係y=fx嘅關係 out of blanket 唔影響x-axis所以上下(depends on positive or negative)
Inside blanket同倍大倍細相同理解方法

:^(

理解完 你都係去死記啦

:^(

考試講求速度

Really?

We know that y=x is the mid-point locus between y=e^x and y=lnx

Locus同inverse function好似兩樣野嚟

:^(

Exponential function太perfect啦你個例子太特別
打個比喻我求其畫嘅一條locus佢可以冇inverse

Inverse一定有
只係inverse不一定係function

Try to invert y = e^(-x^2)

x = e^(-y^2)

仔細啲睇清楚人哋留言先啦好唔好

Original graph:
[img]https://img.eservice-hk.net/upload/2017/09/27/013305_4a47a0db6e60853dedfcfdf08a5ca249.png[img]

When inverted:
[img]https://img.eservice-hk.net/upload/2017/09/27/013320_fb5c81ed3a220004b71069645f112867.png[img]
Something like this

屌 巴打們唔好同龜sir認真
佢會入去啲DSE Post叫人solve sin x=2

:^(

親身例子

:^(

我自己就係數學超差果種人，背公式對我黎講真係好困難。一黎會同其他相似既式撈亂，果啲xxyy記到亂晒，係我心目中全部都係一樣，到依家連sin cos tan都成日搞錯

:^(

二黎就真係莫名其妙地入唔到腦，呢頭背完十分鐘後就唔記得，相對地中文就記得幾快。
數學於我仲有個難處就係唔識靈活用，照書跟例題㩒cal機，識做。去到exercise頭一兩條淺既可能識，之後就收晒皮

:^(

只要換個同例題唔同/換個問法就仆街，例如我識左x+2=5，但係我唔知x=幾，理解唔到點換

:^(

Inverse一定有
只係inverse不一定係function

Try to invert y = e^(-x^2)

x = e^(-y^2)

仔細啲睇清楚人哋留言先啦好唔好

Original graph:
[img][url]https://img.eservice-hk.net/upload/2017/09/27/013305_4a47a0db6e60853dedfcfdf08a5ca249.png[img][/url]

When inverted:
[img][url]https://img.eservice-hk.net/upload/2017/09/27/013320_fb5c81ed3a220004b71069645f112867.png[img][/url]
Something like this

屌 巴打們唔好同龜sir認真
佢會入去啲DSE Post叫人solve sin x=2

:^(

佢成日衝出嚟
忍唔到口要話一話佢

:^(

x = e^(-y^2) is not a function of x since both y=m and y=-m (for arbitrary m) points to same value.

屌 巴打們唔好同龜sir認真
佢會入去啲DSE Post叫人solve sin x=2

:^(

每次做啲數問我f(x)+1/f(x+1)/2f(x)係褪上定褪落定係乘大左都要let一次f(x)=x^2 plot 一次先知

:^(

:^(

:^(

我理解唔到呢個

:^(

Btw function fx有equation就好易做

:^(

醒目

When x is replaced by x+1,
x_new +1 = x_old

So, new value of x is less than the original by 1
The graph is translated leftwards 1 unit.

大概係咁解

喔

:^(

明啦 我以為個/係除號
原來係講緊transformation

:^(

我理解方法係y=fx嘅關係 out of blanket 唔影響x-axis所以上下(depends on positive or negative)
Inside blanket同倍大倍細相同理解方法

:^(

理解完 你都係去死記啦

:^(

考試講求速度

考試還考試，我認同考試係要背表嘅
但如果你無學過點解，成個課程咁多書都只會係白讀

:^(

屌 巴打們唔好同龜sir認真
佢會入去啲DSE Post叫人solve sin x=2

:^(

嘩屌

:^(

真心咩咁樣誤人子弟法
未見識過

係舊登見到一D DSE雞好串先忍不住出solve sin x=2串鳩佢地姐

:^(

:^(

每次做啲數問我f(x)+1/f(x+1)/2f(x)係褪上定褪落定係乘大左都要let一次f(x)=x^2 plot 一次先知

:^(

:^(

:^(

我理解唔到呢個

:^(

Btw function fx有equation就好易做

:^(

醒目

When x is replaced by x+1,
x_new +1 = x_old

So, new value of x is less than the original by 1
The graph is translated leftwards 1 unit.

大概係咁解

喔

:^(

明啦 我以為個/係除號
原來係講緊transformation

:^(

我理解方法係y=fx嘅關係 out of blanket 唔影響x-axis所以上下(depends on positive or negative)
Inside blanket同倍大倍細相同理解方法

:^(

理解完 你都係去死記啦

:^(

考試講求速度

考試還考試，我認同考試係要背表嘅
但如果你無學過點解，成個課程咁多書都只會係白讀

:^(

就係transformation

:^(

啱啱唔記得佢叫咩名

:^(

之前quiz背過依家又亂曬

:^(

同埋 (just for reference)
y(x+i) 點 transform (i^2 = -1)