FUNCTIONS: The problem when learning Inverse Functions

(Since my time is limited, so for every chapter I will skip some and only focus on parts which most of the students found problem with it. Maybe after I retire, then only I will complete those skipped parts.)

For a lot of Malaysia high school students,
the first problem that they faced in Addmaths is usually when learning the Inverse Functions.

WHY???

This is because many teachers rushing to finish teaching all the syllabus,
so they couldn't spend too much time on explaining Inverse Functions.

Let us use an example.

If f(x) = x/3 +4 ,
then what is the Inverse Function of f ?

Well,
a lot of teachers will start with Let y =........

The 1st reaction from the students:

?????

Let y what ?????

Isn't that f(x) = x/3 +4 ???

Why suddenly became y = x/3 +4 ???

Some students stuck at here,

and thus starting to feel that Addmaths is hard..................

If they could hang on it and continue:

Let's skip the process,
at last the teacher will show this:

Most of the student will think that that's the end,
but suddenly the teacher said at the end we need to write like this:

Students again ????

Why did the x at the left became so complicated??

Isn't that 3y-12 at the right hand side??
Why suddenly became 3x-12 ??

Thus....................

Just a lesson about Inverse Functions...............

A lot of ??? started to appear in student's mind,
and started to think that Addmaths is from another planet.

Especially in Malaysia,
a lot of students started to have issues with Addmaths starting this part.

As more and more lessons went on,
more and more that students do not understand,
and the worse their Addmaths result became.

This teaching method of Inverse Functions which is too time-saving without explanation,
again used by a whole new generation of teachers,
and thus causing more students to have problem with it...............

A vicious circle!!!

So what is the solution?

First,
teacher must be patient and cannot too rush on trying to finish the syllabus.

Teacher need to spend time to explain until the students understand,
especially the Let y,
and the final answer part.

I will share about how I teach the Inverse Functions at next chapter,
which I combined my experience of teaching different high school syllabus.
(SPM, IGCSE, UEC etc.)

Thank you!

End.

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Related articles:
Composite Functions


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FUNCTIONS: Composite Functions (SPM, IGCSE, A-LEVEL...)

(Since my time is limited, so for every chapter I will skip some and only focus on parts which most of the students found problem with it. Maybe after I retire, then only I will complete those skipped parts.)


Since the 1st chapter of Additional Maths in Malaysia high schools is FUNCTIONS,
so I will start from it!

Let's start with something easy,
f(x) = x+7 ,
so what is f(2):

Answer:
(I always like to use different colour.)

Thus,
we found that f(2) = 9 .

Next,
a bit more complicated:

Answer:

Alright!
Warm up done!
Is time to enter today's topic.

So.... Composite Functions.

Basically,
it is like we try to combine different functions into one.

How to do it?
We will use the f(x) and g(x) from above as example,
first we find fg(x):

Answer:

Thus,
we found the Composite Function of fg, which is fg(x) = 3x+2 .

Now,
how about gf:

Answer:

Here is something important,
gf doesn't equal to fg.
(Unless special case.)

Not only f and g can form composite function,
f can form composite function with itself too:

Answer:

DONE.

You can try to find gg if you want.

The answer of gg is 9x-20 .

That's all the basic about Composite Functions.

Of course,
even if you understand all these,
it doesn't mean that you can get full marks in your exam.

UNDERSTANDING is just UNDERSTANDING,
SOLVING QUESTION is different.

At least if you understood,
it will help you a lot in solving questions.

Maths should be learnt easily,
Practice should be done accordingly,
exam should be faced seriously.

Thank you!

End.

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MY MATHS BLOG(Chinese ver.)
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The reason why I started this blog

"Our school Maths teacher just copied the formula on the white board,
then teacher tried to solve the question,
but never get the correct answer."
The student complaint to me.

"Well.....
teacher is still a human, not perfect,
sometimes they will make mistake too."
I said.

"Not sometimes, is A LOT OF TIMES!"
The student complaint again.

"......................"
I was speechless.

Above was the conversation between me and a student who I started to do home tuition with her at the 1st lesson.

I am Leon, a full time home tutor.

After graduating from university,
I became full time home tutor right away.

I taught Maths and Chinese language at the beginning,
but later on I decided to focus on Maths only.

Year 2019 is the 9th year of me teaching home tuition.

As a home tutor,
I didn't get to meet a lot of students,
but most of them are facing problems in learning Maths.

THUS,
is not hard to imagine that for the whole country of Malaysia,
or even the whole world,
there A LOT MORE students having trouble with Maths.

I only able to help a limited number of students every year,
so what should I do if I wish to help more students??

THAT'S WHY I STARTED THIS BLOG.

For teacher,
even though the teaching way I shared at my blog might not be the best way,
but it is still based on my teaching experience of the past 8 years,
so feel free to take it as reference.

For student,
I hope that when you have problem in learning certain Maths subject,
you will be able to find solution here.

This blog will be based on ICCSE, A-LEVEL and SPM.
(since I am based at Malaysia)

Since my main job is still home tuition,
so this blog will not be my main priority,
but I will try my best to update it.

Thanks for reading.

Please LIKE MY Facebook Page & FOLLOW MY TWITTER to be updated with the blog.



Important Links:
CONTACT ME
ABOUT ME
MY MATHS BLOG(Chinese ver.)
MY YOUTUBE


Feel free to e-mail me if you have any problems:
leonleongmaths@gmail.com