(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 learning how to find Inverse Functions,
is better to understand the following concept:
If f(x) is going from point A to point B:
Then:
From point B to point A will be the Inverse Functions.
Let's take a proper example:
Answer:
f(9) = 7
So how the 7 get back to 9 ?
Let's take a look at just now how the 9 get to 7:
9 divided by 3,
then plus 4,
become 7.
Reverse the process.
7 minus 4,
then multiply with 3,
become 9.
By picture:
minus 4 first then multiply by 3,
which is our Inverse Function.
minus 4, so is x-4.
Then multiply by 3, so (x-4) x3 , or can write as 3(x-4).
Don't believe?
Let's use 7 to see whether can get back 9 or not:
Answer:
Yes,
we did get 9.
Another interesting part of Inverse Functions:
Answer:
We will get back x at last.
During exam,
I strongly recommend the above method to check whether the inverse function you found is correct or not.
If you can get back x,
then is 100% correct.
Just like you walk 10 steps above from your house, then 15 steps to the right, stop.
And then you walk 15 steps to the left, reverse 10 steps, stop.
You will be back to your house.
Similarly,
the x goes through function, and then inverse function,
will be x again.
Oh yeah,
you can try this by yourself:
The answer for sure is x.
Of course,
the above are all explanation only,
not the standard format of answering exam question.
Especially if you face this type of question:
What should we do?
I will share about the standard solution at next chapter.
Thank you!
End.
Please LIKE MY Facebook Page & FOLLOW MY TWITTER to be updated with the blog.
Related articles:
Composite Functions
Inverse Functions(1)
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
No comments:
Post a Comment