C3 Functions help

Fraggr

Fraggr

Fraggr

Soldato
Joined
29 Jun 2006
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Sheffield
Feel slightly ashamed to actually be asking this...

I'm doing some C3 revision atm, and I'm stuck on a pretty simple question. I'm sure it's just a mind blank or something, but how do you find the inverse of:

f: x -> 2x+3 / x-1 { x E R, x > 1 }

Workings please! I know the answer is x+3 / x-2 { x E R, x > 2 } :)
 
simples:

re-arange the equation so you have x=, then swap the x and f(x) terms.

working to follow:


for demonstration let f(x)=y
y = (2x+3)/(x-1)

xy - y = 2x + 3 .....(multiplied both sides by (x-1))
xy - 2x = 3 + y ......( gather all x terms on one side)
x*(y-2) = (3+y) ......(factorise out the x on the LHS)
x = (3+y)/(y-2) ..... (divided both sides by (y-2))

here is the trick, now you swap x and y for each other and let y= f^-1 (x)

y = (3+x)/(x-2)
f^-1 (x) = (3+x)/(x-2)
 
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Edit: Damn beaten :(

Nice ninja edit there vertica :p
 
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The working i initally posted was correct...for the question i copied down :p

I just copied the question down wrong. lol
 
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Thanks guys. Completely forgot about factorisation :p

Another cheeky little question... Again, have the answer. It is APPARENTLY 49/52. However, everyone is getting varying answers... Even a further maths student who is planning on doing maths at cambridge doesn't get 49/52.

"A card is selected at random from a normal set of 52 playing cards. Let Q be the event that the card is a queen and D the event that the card is a diamond. Find: P(Q' U D)"
 
dug out my notes now cos this was annoying me..

so you need the formula:

P(Q' U D) = P(Q') + P(D) - P(Q' n D)

so here you have:

P(Q') = 48/52
P(D) = 13/52
P(Q' n D) = 12/52

so combining these as above you get 1/52(48+13-12) = 49/52

so there you go

ps, its obviously not all about Cambridge maths, i'm at Durham doing it ;)
 
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OMG! I had the right idea, but accidentally put 1/13 not 13/52 as P(D).

Thanks, just confirmed my method was right. :)
 
I am happy to say I have blanked all this maths from my memory. Unfortunately doing A Level/Highers Maths has also killed my ability in arithmetic lol
 
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