FUNCTIONS: How to find Inverse 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.)

Before starting to learn how to find Inverse Functions,
please have a look at this:

The function in the picture can be written as f(x) = y .

Thus:

If we reverse it,
it will become:

The above relation must be kept in mind!!!

Now,
let's learn how to find Inverse Functions:

Wait a moment!!

As a teacher,
we teach to make sure the students understand,
not to show off about our knowledge,
so let's use a simpler example:

Answer:

STOP!!!

How was it?
A mixture of both f(x) and x,
very confusing right??

That's why!

We let y to replace the f(x):

What?
You don't like y?
Okay, which letter do you like?
e? k? m? w?

No matter which letter you use,
you will get the same thing at last.

HOWEVER,

In Maths world,
x and y always appear together, like husband and wife,
do you really want to be so cruel to make x and y to be away from each other??

Also,
if you use other letter instead of y,
your Maths teacher most probably will not be happy about it.

We want to be relax and happy at learning Maths,
so why want to make someone unhappy just because of a letter?
Right?

Alright!
Let's continue with y and the x = 3(y-4).

Remember what I emphasized just now:

So the x at the left hand side will be replaced as:

Here comes the problem,
In Maths world,
x is like the greatest existence, the greatest of everything, the supreme being!

Even though the above function can be answer already,
but how dare you ignore x !!!

Especially your Maths teacher will not be happy if you ignored x,
and your marks will be minus during exam,
since you ignore x, the supreme being!!

I said before,
the most important thing in learning Maths is to be relax and happy.

Yes,
is good to have your own opinion.

HOWEVER,

if you too insisting on certain thing,
then is called as STUBBORN.

So just relax and follow the Maths world,
change all the y to x.

Then your Maths teacher will be happy,
and you can protect your exam marks,
isn't that better?

Come,
let's change all the y to x at final answer:

That's all about how to find the Inverse Functions.

Of course,
you don't have to write so many things when you are answering the question,
just write like what your Maths teacher taught you.

What?
Need me to explain one more question?

Alright!

I will use the more complicated question:

Answer:
(There are blue colour and red colour,
the blue colour is the one I will write down when answering,
the red colour is the one just appear in my brain and do not really need to write down.)

Done.

Since the red colour parts only appear in my brain,
so I only write like this when answering a question:

That's all the basic about Inverse 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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Related articles:
Composite Functions
Inverse Functions(1)
Inverse Functions(2)


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