Question

if f(x)=-6x+6, then f^-1(x)

Answer 1

any attempts?

Answer 2

solve
\[x=-6y+6\] for \(y\) in two steps

Answer 3

that's what I was thinking.. swap the variables.. solve for y and then replace y with the f inverse notation .

Answer 4

at least that is the math teacher way
the thinking way is to recognize that\[f(x)=-6x+6\] means
a) multiply by \(-6\) then
b) add \(6\)
inverse will do the opposite operations in reverse order

Answer 5

but solving \[x=-6y+6\] for \(y\) takes two steps, so it is just as quick as thinking

Answer 6

I'm confused

Answer 7

can you work through it with me?

Answer 8

please? all my attempts arent working out

Answer 9

@UsukiDoll

Answer 10

Just follow these easy steps:

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 11

I know the steps but I usually get stuck when solving for y

Answer 12

\[y=-6x+6 \]
\[x=-6y+6\] what would your first step be to solving for y?

Answer 13

Try your best, don't be afraid to make mistakes

Answer 14

get rid of + 6 by subtracting six from both sides

Answer 15

There you go, good job, so we have \[x-6 = -6y\] now what?

Answer 16

divide by negative 6

Answer 17

Good! \[y = \frac{ -(x-6) }{ 6 }\] you may simplify that now

Answer 18

how?

Answer 19

As in you can distribute the negative sign, and get \[y = \frac{ -x+6 }{ 6 } \implies \frac{ 6-x }{ 6 }\] so what's our final step?

Answer 20

What should we replace y with :)

Answer 21

the rule for negative functions

Answer 22

\[f^{-1}(x) = \frac{ 6-x }{ 6 }\] yup :)

Answer 23

Not so bad right? Just have to try it and you'll start getting it!

Answer 24

it helps to talk it out, I probably would've taken a lot longer to get that on my own

Answer 25

I think that is the best way of learning to :)

Answer 26

thanks for your help, i understand it better, not completely yet but making progress

Answer 27

No problem, take care!