1. ## god

i feel pretty good about my calculus III final. only i know i got one question slightly wrong. to integrate a function we had to find an inverse function, i KNOW that i got it wrong but i still cant understand WHY i got it wrong.

the function was the square root of x/3. i had the inverse function as 9x^2. the right answer is 3x^2 but i cant understand why. in the original function, you take x, divide it by three and take the root of EVERYTHING. its inverse should: take x, multiply it by 3 THEN square everything. 9x^2. but i can compute some examples and show that 3x^2 IS the right inverse, but cant figure out where my reasoning is wrong.
you multiply it by the root of three and then square everything, not three.

2. well, yeah, obviously that is a way to get the right answer, i still dont fully understand where my reasoning was wrong. did i do the 'order of operations' if you will wrong? like, do you not only have to do inverse operations but also in the reverse order.

for example: original function: take x, divide it by three, take square root of everything. therefore, inverse function: take x, square everything, multiply by three, in that order. this is probably it.

3. I always just go from y=sqrt(x/3) and then swap x and y and then solve for the new y.

4. yes, there are many ways to get the right answer, none of which i did because i was somewhat rushed and just did what seemed logical. i know that it was wrong, and i know things to do that would have gotten me the right answer, but just was questioning what was wrong in my particular line of reasoning.

5. out of curiosity rayne, how far have you gotten in math topics so far

6. Originally Posted by God
yes, there are many ways to get the right answer, none of which i did because i was somewhat rushed and just did what seemed logical. i know that it was wrong, and i know things to do that would have gotten me the right answer, but just was questioning what was wrong in my particular line of reasoning.
Oh, then I'd need a pen and paper, but I don't think I have any so I'll leave Rayne to answer.

7. Originally Posted by God
well, yeah, obviously that is a way to get the right answer, i still dont fully understand where my reasoning was wrong. did i do the 'order of operations' if you will wrong? like, do you not only have to do inverse operations but also in the reverse order.

for example: original function: take x, divide it by three, take square root of everything. therefore, inverse function: take x, square everything, multiply by three, in that order. this is probably it.
yes you have to do it in the reverse order

8. a better way to think about this problem is instead of taking it in terms of √(x/3) imagine it to be 1/√3 times √x - ie, take the root of x and then divide it by root three. to get back the original function do the step in reverse: multiply it by √3 and then square everything.

so the inverse function is (x√3)^2 which is 3x^2.

you should generally avoid making taking the root of constants a part of the function. just imagine the roots as one whole constant. it prevents shit from hitting the fan; roots are pretty finicky.

9. Originally Posted by God
out of curiosity rayne, how far have you gotten in math topics so far
basically finished around 80% of whats there in khanacademy's maths stuff the exceptions being bits of calculus and linear algebra and a lot of advanced statistics.

side note: i might fail my maths exam.

10. what are your math exams like? i dont suppose you have any sort of practice exam sort of thing file online?

11. When in doubt reverse the order.

12. A stitch in time saves nine.

13. Originally Posted by God
what are your math exams like? i dont suppose you have any sort of practice exam sort of thing file online?
http://cbse.nic.in/curric~1/sqpms-ma...2010-part1.pdf

two sample papers and solutions

14. Originally Posted by Rayne
I have to use this.

15. I lost 3 minutes that I'll never get back reading that.

16. Originally Posted by Lord Trigon
I lost 3 minutes that I'll never get back reading that.
Typically time spent is always time lost, seeing as you can't regain it.

17. The concept of taking Calc III makes my soul bleed.

18. Originally Posted by Seven
Typically time spent is always time lost, seeing as you can't regain it.
true but you know what is a good read, looking up poisonous plants. I found out I had collected nightshade when I was a kid.

19. Originally Posted by Rayne
btw did you actually try doing these? i think youve covered most of the shit in it.

20. ??

a YES or NO would suffice

21. not really. i should though.

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