Pure Maths Yr 2: Composite Functions, Domain/Range Exam Question
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- เผยแพร่เมื่อ 6 ก.ย. 2024
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In this video I explain how to solve an A grade question on:
1. Finding the domain and range of a function.
2. Finding a composite function.
3. Finding the domain and range of a composite function.
![[กูเพิ่งซื้อมึงปิดหนี] 20 นาที ผมรีวิวเกมที่แย่ที่สุดในโลก CONCORD](http://i.ytimg.com/vi/XhC-3q3Ii7I/mqdefault.jpg)
do more hard A grade questions like these and you'll end up boosting everyone's grades and more views :)
Yo, theres something bothering me about this.
You got the domain of g(x) as >5 which sorta made sense.
But i've been practicing loads of composite functions past paper question and almost always the domain of fg(x) would be the domain of g(x). If it was gf(x) the domain would be the same as f(x) too.
So, I did this question myself and I came to domain is >3 (or, as I like to put in interval notation (3, infinity))
So, I had the range of (12, infinity). Since the domain is limited to 3, plug 3 into 4xsqared -8x to get 12.
Making the domain into 5 to infinity has really confused me about all the other questions I've been working out.
I swear, someone is wrong somewhere. I really hope it's me but I'm become more doubtful of that the more I try to understand the range of a composity function.
I think ur right bro
Hi, so fg(x) = (2x - 2)^2 - 4 = 4x^2 - 8x
The domain of fg(x) is the intersection of the domain of g(x) and the domain of fg(x).
Now the domain of g(x) is x > 3, and the domain of fg(x) shows no apparent restriction, so at the moment we just have x > 3. However, as f(x) also has a restricted domain, we need to check if all of the values of g(x) can be substituted into f(x).
If x = 4, for example, then it can be substituted into g(x) to get g(4) = 6. But then 6 cannot be substituted into f(x) as it has a domain of x>8.
So g(x) > 8, 2x - 2 > 8, so x > 5.
So the domain of fg(x) is x ∈ ℝ, x > 5.
When x = 5, fg(5) = 60. fg(x) describes a parabola with a vertex at (1,-4). So the range of fg(x) is fg(x) > 60
So the blue part of the curve here is fg(x): www.desmos.com/calculator/oaccqawzse
His method is right and his method is the same method which is on madas maths
My g!!!!! Miss those days Zeeshan! Ur an amazing teacher! Keep it up bro, you’ll go far in life iA!
Ashjath Aabith Mr Aabith! Thank you for the kind comments. Your group was a pleasure to teach. Hope you’re keeping well 👍🏻
I still dont quite understand how u found the domain and range for fg(x). Can someone pls explain :(
Thank you so much I think I finally get composite functions.
In a situation with an exponential function such as: 3 modulus 2^x - 1 = 2^x, where you're expected to solve for x, what would you do? The modulus of 2^x -1 gives you the same result as 2^x - 1 since there is nothing below the x axis.
Your content is awesome and easy to follow
sir why is x>3 and x>5 just x>5? what happens to 4 and 5 values
When will you be back on the whiteboard? I miss that!
Smith Houston as soon as college reopens I’ll be back on the whiteboard 👍🏻
life saver
For me, fg does not exist so we cannot find fg and the domain of fg. It is because the range of g is not within the domain of f. gf does exist since the range of f is within the domain of g so we can find gf and its domain.
how many minutes to answer this question in exam conditions
thank you
2:15 where did you get 60 from????
Substitute x =8 and you will get 60 for y
i don't understand where 60 came from, in the first question
He put 8 into the equation to find what y is when x=8
Very helpful video but would’ve been better without the music
Hello, will you be making any videos on Vectors A2 Chapter 12?
Siddika Begum for sure, I will be covering all four textbooks. Pure 1 and 2, Applied 1 and 2.