Pure Maths Yr2: Domain and Range of Composite Functions

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Zeeshan Zamurred

Күн бұрын

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@sultanashahjalal5364 4 жыл бұрын

hands down, the BEST a level maths channel on youtube. idc what anyone else says

@armanitwahafa4758 Жыл бұрын

Exactly what I've been looking for✨ Thank you❤️

@nasimahmed3570 4 жыл бұрын

Your method was so much faster and simpler than my teachers

@naveedahmed7336 3 жыл бұрын

You have an excellent knowledge and know how to explain

@spartan5000000000000 3 жыл бұрын

Is the question correct? Based on the definition of a composite function f(g(x)) does not exist for the given domain. For f(g(x)) to exist the range of g(x) should be a subset of the domain of f(x). Range of g(x)

@koushikrajsaha5118 10 ай бұрын

You said that domain of g is less than equals to 8, which is correct. g is a decreasing function. Input to g has to be > 8. No problem there. And Input to f has to be < 0. In this case, the input to f is g. So he formed an inequality to find the range of values of x for which g is < 0. The new domain is x > 24. Now 2 conditions have to be fulfilled for domain of fg. That is x > 8 and x > 24. Again here are no contradictions and a new combined inequality can be formed for the domain of fg. If you illustrate x > 8 and x> 24 on a number line, you will see the combined inequality is x > 24 . So that is the domain for fg(x). He is correct. Range of g is g

@koushikrajsaha5118 10 ай бұрын

You are wrong. Domain of fg is x > 24. Lets verify if your answer for the domain is correct or not. For fg(x) -----> lets put a value of x > 8 say 10, so g(10) = 7. Now you have to do f(7) which you cant do because input to f is x < 0. Now there is a contradiction. But say you take a value of x > 24 for domain of fg(x), say 26 for e.g. so g(26) = -1 Now you have to do f(-1) and now this is possible because as mentioned in the question, input to f is x < 0 and -1 is less than 0, which is a mathematical fact. So if you say that the domain of fg(x) is x > 8, that is wrong. Two conditions need to be fulfilled for the domain of fg(x) 1. x > 8 because the function g acts first on x. 2. The domain of f(x) has to be within the range of g(x) and whatever you put inside f has to be less than 0. In this case fg(x), so input to f is g(x), which means g(x) < 0.

@KungFuBarbie-pc7hb 4 ай бұрын

@@koushikrajsaha5118does this method always work pls help

@koushikrajsaha5118 3 ай бұрын

@@KungFuBarbie-pc7hb Yes it will help. Do you need any more help?

@lolumslolla9451 4 жыл бұрын

Jazakhallah for this sir

@kylezinho_ 4 жыл бұрын

These videos are super useful, cheers

@theadventurer7259 8 ай бұрын

Excellent explanation

@bilal5705 2 жыл бұрын

makes so much sense thanks

@itstheassessment3859 4 жыл бұрын

Hello,when are you going to start doing GCSE stuff?

@yortlj 2 жыл бұрын

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@monskree8053 2 жыл бұрын

bro im ur biggest fan

@trigobrooken6260 3 жыл бұрын

THANK YOU SOO MUCH

@kakoly7697 2 жыл бұрын

Your both answers are wrong. Domain of fg(x) is x>8. And range of fg(x) is fg(x)>48. This is because range of g(x) is the domain of f(x) which is the domain of fg(x).

@moniralamin7694 2 жыл бұрын

Ohh yes I also got the same answer like you... Thanks a lot. And this guy solve both maths incorrectly 😂😂

@koushikrajsaha5118 10 ай бұрын

@@moniralamin7694 You are wrong. Domain of fg is x > 24. Lets verify if your answer for the domain is correct or not. For fg(x) -----> lets put a value of x > 8 say 10, so g(10) = 7. Now you have to do f(7) which you cant do because input to f is x < 0. Now there is a contradiction. But say you take a value of x > 24 for domain of fg(x), say 26 for e.g. so g(26) = -1 Now you have to do f(-1) and now this is possible because as mentioned in the question, input to f is x < 0 and -1 is less than 0, which is a mathematical fact. So if you say that the domain of fg(x) is x > 8, that is wrong. Two conditions need to be fulfilled for the domain of fg(x) 1. x > 8 because the function g acts first on x. 2. The domain of f(x) has to be within the range of g(x) and whatever you put inside f has to be less than 0. In this case fg(x), so input to f is g(x), which means g(x) < 0.