SRL Archive - Mathematics

It seemed simple at first but I cant seem to make X the subject of this formula. :|
a = (2x + 1) / (x + 2)

I've managed to rearange it so that there is only one x:
a = 2 + (5 / (x - 2))

What do I do after that?

The actual question was to find the equation of ƒ^-1(x) when ƒ(x) = a.

~
I dont have access to a computer atm so refrain from posting attached files unless it in necessary ty =)

switch x and a then solve for x.

well you could use this website if you don't need the work
http://www.wolframalpha.com/input/?i=%282x%2B1%29%2F%28x%2B2%29%3Da
they show it as the answer being:
x = (1 - 2a) / ( a + 2)

Umm Im not sure what you mean by that… bolshak
I need x in terms of "a" … preferably with only one "a" term.

Edit: thanls thisguy but i need to know how to work it out .. there seems to be no working out in this one

From: logical
Umm Im not sure what you mean by that… bolshak
I need x in terms of "a" … preferably with only one "a" term.

Edit: thanls thisguy but i need to know how to work it out .. there seems to be no working out in this one

F^-1X = Inverse of F'(x)

They're asking you for the inverse function..

y = 1/x.. inverse would be x = 1/y.. When you swap a with x, just solve to isolate a again. that's it.

From: ggzz
F^-1X = Inverse of F'(x)

They're asking you for the inverse function..

y = 1/x.. inverse would be x = 1/y.. When you swap a with x, just solve to isolate a again. that's it.

but the "2+" makes things more complicated than simply swapping the two:
for x = 1/y
multiply the equation by y
xy = 1
and divide by x
y = 1/x

however with x = 1/y + 1 :
multiply by y
xy = 1 + y
divide by x
y = (1 / x) + (y / x)
y = (y + 1) / x
… it doesn't work as well.
still stuck .. unless some1 posted in the age ot took tp type this on a 3ds ›.‹

Bleh I'm bored.
a = (2x + 1) / (x + 2)
a(x+2) = 2x+1 (multiply both sides by x+2 to get rid of the fraction)
ax+2a = 2x+1 (get rid of brackets)
ax=2x-2a+1 (substract 2a from both sides to get 2a to the other side)
ax-2x = -2a+1 (substract 2x from both sides to move it to the left)
x(a-2) = -2a+1 (everything on left side is multiple of x, so we take x out of brackets)
x = (-2a+1)/(a-2) (divide both sides by a-2)

For this kind of stuff (high school math I assume), this always works:
Get rid of the fraction, by multiplying both sides by it (not by using long division, though that would work but it's ugly and requires work)
Every term with X at one side (in this case left side), everything else right side
Factor X out, so you get x(…) = …
Divide both sides by the term after X

The above always works for this kind of excercises. The real trick is moving everything with X to one side and everything else to the other side.

ah! silly me… done the division coz i learnt it recently and assumed that was what i was meant to do, misleading me :P
Thats my excuse anyway :).
Ty Markus =D

From: Markus

ax=2x-2a+1 (substract 2a from both sides to get 2a to the other side)
ax-2x = 2a+1 (substract 2x from both sides to move it to the left)

Made a mistake here, you dropped the "-" in front of the 2a in the second line, would still get all the method marks though ;P