Question

i need some help

Answer 1

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

Answer 2

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

Answer 3

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]

Answer 4

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

Answer 5

yes

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

Answer 6

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

Answer 7

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

Answer 8

y-1/2=x

Answer 9

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?

Answer 10

you can do it!

Answer 11

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

Answer 12

x=y/2-2/1

Answer 13

??

Answer 14

idk im lost

Answer 15

thats what i thought

Answer 16

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

Answer 17

yes

Answer 18

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

Answer 19

and thats what u want me to find for my prob

Answer 20

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
\(x=(1/9)(y +3)\)

Answer 21

yes

if you truly have not been shown how to do this algebra, then you should really not be trying to do inverse functions...

Answer 22

i must have missed that class but yeah

Answer 23

well copy what i did and see how you go.

Answer 24

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

Answer 25

very good

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

Answer 26

yes
3

Answer 27

what happens now

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

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

\(f^{-1}(2) = (2)/2 + 3\)

Answer 32

okay i think i get it

Answer 33

so doo i solve f−1(2)=(2)/2+3

Answer 34

yes

Answer 35

f=1/2

Answer 36

no thats wrong

Answer 37

yes, go again

Answer 38

5

Answer 39

-5

Answer 40

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

Answer 41

im lost a little

Answer 42

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

Answer 43

so i just solve the answer part