anonymous
  • anonymous
i need some help
Mathematics
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anonymous
  • anonymous
i need some help
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
1 Attachment
IrishBoy123
  • IrishBoy123
|dw:1441715548469:dw|
IrishBoy123
  • IrishBoy123
have you got your equation for \(f^{-1}(x)\) yet??

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anonymous
  • anonymous
idk how to do anything with it my teacher never taught me how
IrishBoy123
  • IrishBoy123
first, we'll re-write your equation as y = 2x - 6, so this takes in x values and returns y values now switch that around so that it says x = ... ie give me an equation that takes in y values and returns x values [you'll see what the point of this is when we're done]
anonymous
  • anonymous
so takes in is the 2x-6 part and puts out is y=
IrishBoy123
  • IrishBoy123
yes now switch it around so it says x = ....
IrishBoy123
  • IrishBoy123
example y = 2x +1 x = y/2 - 1/2
IrishBoy123
  • IrishBoy123
example y = 9x - 3 x = (1/9) (y+3)
anonymous
  • anonymous
y-1/2=x
IrishBoy123
  • IrishBoy123
example i start with y = 2x +1 i switch around to get x = y/2 - 1/2 example i start with y = 9x - 3 i switch around to get x = (1/9) (y+3) you are starting with y = 2x - 6 can you switch it around in same way?
IrishBoy123
  • IrishBoy123
you can do it!
IrishBoy123
  • IrishBoy123
i can do the first example is steps, if that helps??!!
anonymous
  • anonymous
x=y/2-2/1
IrishBoy123
  • IrishBoy123
??
anonymous
  • anonymous
idk im lost
anonymous
  • anonymous
thats what i thought
IrishBoy123
  • IrishBoy123
x=y/2-2/1 for you question?!?!?
anonymous
  • anonymous
yes
IrishBoy123
  • IrishBoy123
i'll try this 1st example \(y = 2x +1\) add -1 to each side \(y-1 = 2x +1-1\) so \(y-1 = 2x\) divide each side by 2 \(y/2-1/2 = 2x/2\) so \(y/2-1/2 = x\) just switch left hand and right hand sides around \(x = y/2-1/2\) and that is done
anonymous
  • anonymous
and thats what u want me to find for my prob
IrishBoy123
  • IrishBoy123
2nd example \(y = 9x - 3\) add 3 to each side \(y +3= 9x - 3+3\) so \(y +3= 9x \) divide each side by 9 \((1/9)(y +3)= 9x/9\) so \((1/9)(y +3)= x\) switch around \(x=(1/9)(y +3)\)
IrishBoy123
  • IrishBoy123
yes if you truly have not been shown how to do this algebra, then you should really not be trying to do inverse functions...
anonymous
  • anonymous
i must have missed that class but yeah
IrishBoy123
  • IrishBoy123
well copy what i did and see how you go.
anonymous
  • anonymous
x=(y/2)+(2/6)
IrishBoy123
  • IrishBoy123
very good we can simplify a little, ie the 2/6, right?
anonymous
  • anonymous
yes 3
anonymous
  • anonymous
what happens now
IrishBoy123
  • IrishBoy123
i'll do this bit as it's just notation, important notation but you havealready done the hard bit you recall we took your function \( f(x) = 2x - 6\) and re-wrote as \( y = 2x - 6\) so we could manipulate it a bit easier well we now take your solution for the inverse ie \( x=y/2+3\) and we re-write it as \(f^{-1}(x) =x/2 + 3 \) so or example \(f(3) = 0\), and hey presto \(f^{-1}(0) = 3\)!!! so you now take \(f^{-1}(x) =x/2 + 3 \) and answer the question
IrishBoy123
  • IrishBoy123
they want \(f^{-1}(2)\)
anonymous
  • anonymous
alright i followed and understood upto f(3)=0 and then i got lost
IrishBoy123
  • IrishBoy123
no worries function \(f(x) = 2x - 6 = 0 \implies f(3) = 2(3) - 6 = 0\) inverse function \(f^{-1}(x) = x/2 + 3 \implies f^{-1}(0) = 0/2 + 3 = 3\)!! so we have function f and its inverse \(f^{-1}\). they reverse each other plugging into \(f^{-1}(x) = x/2 + 3\) for x = 2 \(f^{-1}(2) = (2)/2 + 3\)
anonymous
  • anonymous
okay i think i get it
anonymous
  • anonymous
so doo i solve f−1(2)=(2)/2+3
IrishBoy123
  • IrishBoy123
yes
anonymous
  • anonymous
f=1/2
anonymous
  • anonymous
no thats wrong
IrishBoy123
  • IrishBoy123
yes, go again
anonymous
  • anonymous
5
anonymous
  • anonymous
-5
IrishBoy123
  • IrishBoy123
\[f^{-1}(2) = \frac{(2)}{2} + 3\]
anonymous
  • anonymous
im lost a little
anonymous
  • anonymous
what do i do with f^-1(2)
anonymous
  • anonymous
so i just solve the answer part
IrishBoy123
  • IrishBoy123
|dw:1441720473828:dw|
IrishBoy123
  • IrishBoy123
yes just solve
anonymous
  • anonymous
f−1(2)=4
IrishBoy123
  • IrishBoy123
indeed
anonymous
  • anonymous
thats my answer
IrishBoy123
  • IrishBoy123
yes
anonymous
  • anonymous
okay

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