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Help needed on GCSE question (A level topic)

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Can anyone tell me how to do these? We haven't been taught it at school, and the teachers "need to refresh their memory" over half term.

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Original post by Ally-mai

Can anyone tell me how to do these? We haven't been taught it at school, and the teachers "need to refresh their memory" over half term.


gfgf is the shorthand notation for saying g(f(x))g(f(x)) when you substitute the expression of f(x)f(x) into g(x)g(x)

The inverse functions are found by rearranging for xx. So say I have y=4x+1y=4x+1 then my inverse function is x14\frac{x-1}{4}
Reply 2
Original post by RDKGames
gfgf is the shorthand notation for saying g(f(x))g(f(x)) when you substitute the expression of f(x)f(x) into g(x)g(x)

The inverse functions are found by rearranging for xx. So say I have y=4x+1y=4x+1 then my inverse function is x14\frac{x-1}{4}


I still don't understand, sorry. Could you perhaps send me a worked example?
So basically you say sub f(x) into g(x), replacing the xs in g(x) by f(x). For inverse you say y=g(x). You then rearrange to make x the subject. Then you just rewrite the x into g^-1(x) and the ys into xs. Is this further maths gcse? I honestly knew nothing about this topic until I started a2 maths this year but it's fairly simple once you've got your head around it and someone shows you how works. The inverse function basically works so that if you input A and got B from a function, if you input B into the inverse you would get A. The inverse function is also a reflection of the function in the line y=x.
Reply 6
Original post by Ally-mai
We haven't been taught it at school, and the teachers "need to refresh their memory" over half term.

Not sure why they didn't refresh their memories earlier in the year. Did your teacher actually tell you this?
Reply 7
Original post by notnek
Not sure why they didn't refresh their memories earlier in the year. Did your teacher actually tell you this?


The school's maths department decided that it would confuse to many people to teach us it, so I imagine they didn't think they'd have to 'refresh their memories'. And it wasn't my teacher that I asked, but that's basically what she said!
(edited 6 years ago)
Reply 8
Original post by black1blade
So basically you say sub f(x) into g(x), replacing the xs in g(x) by f(x). For inverse you say y=g(x). You then rearrange to make x the subject. Then you just rewrite the x into g^-1(x) and the ys into xs. Is this further maths gcse? I honestly knew nothing about this topic until I started a2 maths this year but it's fairly simple once you've got your head around it and someone shows you how works. The inverse function basically works so that if you input A and got B from a function, if you input B into the inverse you would get A. The inverse function is also a reflection of the function in the line y=x.


No, it's just one of the topics they've added to the new GCSE.
Reply 9
Original post by Ally-mai
The school's maths department decided that it would confuse to many people to teach us it, so I imagine they didn't think they'd have to!

I'm sorry to hear that. Once you've learnt the topic by watching videos I recommend trying as many questions as you can and posting on here if you get stuck.

If you need questions to practice from please tag me tomorrow and I will link you to some that are GCSE Level.
Original post by notnek
Not sure why they didn't refresh their memories earlier in the year. Did your teacher actually tell you this?


I'm not sure which is worse - the fact that they didn't teach it, or the fact that they need to refresh their memory on a simple concept.

I've always imagined that all maths teachers are maths graduates, or graduates in a field related to maths, so surely they should know this topic off by heart anyway and be able to teach it
Reply 11
Original post by RDKGames
I'm not sure which is worse - the fact that they didn't teach it, or the fact that they need to refresh their memory on a simple concept.

I've always imagined that all maths teachers are maths graduates, or graduates in a field related to maths, so surely they should know this topic off by heart anyway and be able to teach it


My school doesn't have a 6th form, so most of the teachers haven't taught this sort of thing for several years. I also know that a fair few of the maths teachers at my school don't have maths degrees. (I know one has a Philosophy degree, where he wrote his dissertation on if numbers were real.)
Reply 12
Original post by RDKGames
I'm not sure which is worse - the fact that they didn't teach it, or the fact that they need to refresh their memory on a simple concept.

I've always imagined that all maths teachers are maths graduates, or graduates in a field related to maths, so surely they should know this topic off by heart anyway and be able to teach it

25% of maths teachers don't have a relevant post A Level degree. And many maths teachers won't have even done A Level maths. That's the way it is nowadays unfortunately.
Original post by Ally-mai
My school doesn't have a 6th form, so most of the teachers haven't taught this sort of thing for several years. I also know that a fair few of the maths teachers at my school don't have maths degrees. (I know one has a Philosophy degree, where he wrote his dissertation on if numbers were real.)


Fair enough, but still doesn't excuse them not preparing for it if its in the spec
You probs just need up to a level to teach GCSE and if you aren't used to notation and haven't done something for 20 years then yeah guess you just forget stuff. No teaching GCSE topics is pretty dumb tho. Screws over kids in less than set1.
Reply 15
Original post by Ally-mai
My school doesn't have a 6th form, so most of the teachers haven't taught this sort of thing for several years. I also know that a fair few of the maths teachers at my school don't have maths degrees. (I know one has a Philosophy degree, where he wrote his dissertation on if numbers were real.)

I don't expect all maths teachers to have maths degrees but I do expect teachers to be confident with a subject before they teach it. They should have relearnt this topic last year and it's sad that their lack of preparation could be detrimental to students like yourself. And I'm sure this is happening all over the country.

If there are any other topics that your school hasn't taught you yet then please let us know so we can help.
Reply 16
Original post by notnek
I don't expect all maths teachers to have maths degrees but I do expect teachers to be confident with a subject before they teach it. They should have relearnt this topic last year and it's sad that their lack of preparation could be detrimental to students like yourself. And I'm sure this is happening all over the country.

If there are any other topics that your school hasn't taught you yet then please let us know so we can help.


I thought that you had to have a degree in maths at least.
Reply 17
Original post by black1blade
You probs just need up to a level to teach GCSE and if you aren't used to notation and haven't done something for 20 years then yeah guess you just forget stuff. No teaching GCSE topics is pretty dumb tho. Screws over kids in less than set1.


The concerning thing is: we are set 1.
(We do technically have 2 set 1s, but neither class has been taught to do this.)
Reply 18
Original post by S2M
I thought that you had to have a degree in maths at least.

Probably less than 30% have maths degrees. There aren't any official statistics for this I don't think. There is a stat that says that 30% of maths teachers don't have a relevant degree in their subject. And I recently found out that a "relevant degree" includes a maths PGCE so their definition of relevant is wildly different to mine.

I consider a relevant degree to be maths/physics/engineering/computer science etc. and I'm sure the percentage that don't have one of these degrees is much higher than 30%.
Reply 19
Original post by notnek
Probably less than 30% have maths degrees. There aren't any official statistics for this I don't think. There is a stat that says that 30% of maths teachers don't have a relevant degree in their subject. And I recently found out that a "relevant degree" includes a maths PGCE so their definition of relevant is wildly different to mine.

I consider a relevant degree to be maths/physics/engineering/computer science etc. and I'm sure the percentage that don't have one of these degrees is much higher than 30%.

Wow, all this time I was completely wrong. I think they should have at least a degree in maths to be able to teach. It'll give them more skills and probably be able to teach better.

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