點解覺得數學公式難背?

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)

其實係唔應該搞咁多步
唔熟general log嘅定義先會咁寫

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

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

讀過3007
覺得諗野個方向好得意

d log同sin cos讀黎真係哂時間
中學個陣放多d時間去英文仲好

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

叻嘅人就會諗到20係4同5嘅LCM
但問題係，對住唔叻嘅人係會睇唔明
我覺得唔係On9,而係因材施教
正如我初學rate and ratio嗰陣都唔會諗到呢條數可以除20，得出x:y=5:4

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

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

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

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

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

佢成日衝出嚟
忍唔到口要話一話佢

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

你呢個例子
我覺得都牽涉到你背嘢嘅方式
可能xyz又係字，123又係字，對你嚟講易混淆(我估啦)
而背嘢都有好多方法嘅
例如唔好用xyz嚟背，試吓🍓🍎🍊呢啲圖案背吖

即係唔好記x+2=5
記 口+🍎🍎=🍎🍎🍎🍎🍎
諗吓兩邊冇咗兩個🍎，口= ?
不過呢啲要配合記得轉加同減/轉乘同除嘅規矩

或者a²-b²=(a+b) (a-b)
記成🍎²-🍊²=(🍎+🍊) (🍎-🍊)
呢個重點係變咗記圖像，唔係文字
同埋記遊戲玩法(+-)
類似玩飛行棋咁，要記得擲到三個六就要返大陸

我可能解釋得唔好，有必要嘅話其他巴絲可以補充吓

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.

一早話咗inverse不一定係function
所以叫你睇清楚先留言

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

雖然我 u 讀 stat
但見到上面 d 式就想嘔

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

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

你覺得係串 其實柒到冇朋友

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)

由2D coordinate plane transform 去 4D geometry?