i need some help

- anonymous

i need some help

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- anonymous

##### 1 Attachment

- IrishBoy123

|dw:1441715548469:dw|

- IrishBoy123

have you got your equation for \(f^{-1}(x)\) yet??

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## More answers

- anonymous

idk how to do anything with it my teacher never taught me how

- 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

so takes in is the 2x-6 part and puts out is y=

- IrishBoy123

yes
now switch it around so it says x = ....

- IrishBoy123

example
y = 2x +1
x = y/2 - 1/2

- IrishBoy123

example
y = 9x - 3
x = (1/9) (y+3)

- anonymous

y-1/2=x

- 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

you can do it!

- IrishBoy123

i can do the first example is steps, if that helps??!!

- anonymous

x=y/2-2/1

- IrishBoy123

??

- anonymous

idk im lost

- anonymous

thats what i thought

- IrishBoy123

x=y/2-2/1
for you question?!?!?

- anonymous

yes

- 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

and thats what u want me to find for my prob

- 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

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

i must have missed that class but yeah

- IrishBoy123

well copy what i did and see how you go.

- anonymous

x=(y/2)+(2/6)

- IrishBoy123

very good
we can simplify a little, ie the 2/6, right?

- anonymous

yes
3

- anonymous

what happens now

- 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

they want \(f^{-1}(2)\)

- anonymous

alright i followed and understood upto f(3)=0 and then i got lost

- 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

okay i think i get it

- anonymous

so doo i solve f−1(2)=(2)/2+3

- IrishBoy123

yes

- anonymous

f=1/2

- anonymous

no thats wrong

- IrishBoy123

yes, go again

- anonymous

5

- anonymous

-5

- IrishBoy123

\[f^{-1}(2) = \frac{(2)}{2} + 3\]

- anonymous

im lost a little

- anonymous

what do i do with f^-1(2)

- anonymous

so i just solve the answer part

- IrishBoy123

|dw:1441720473828:dw|

- IrishBoy123

yes
just solve

- anonymous

f−1(2)=4

- IrishBoy123

indeed

- anonymous

thats my answer

- IrishBoy123

yes

- anonymous

okay

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