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

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

Mathematics
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any attempts?
solve \[x=-6y+6\] for \(y\) in two steps
that's what I was thinking.. swap the variables.. solve for y and then replace y with the f inverse notation .

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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
but solving \[x=-6y+6\] for \(y\) takes two steps, so it is just as quick as thinking
I'm confused
can you work through it with me?
please? all my attempts arent working out
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)
I know the steps but I usually get stuck when solving for y
\[y=-6x+6 \] \[x=-6y+6\] what would your first step be to solving for y?
Try your best, don't be afraid to make mistakes
get rid of + 6 by subtracting six from both sides
There you go, good job, so we have \[x-6 = -6y\] now what?
divide by negative 6
Good! \[y = \frac{ -(x-6) }{ 6 }\] you may simplify that now
how?
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?
What should we replace y with :)
the rule for negative functions
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\[f^{-1}(x) = \frac{ 6-x }{ 6 }\] yup :)
Not so bad right? Just have to try it and you'll start getting it!
it helps to talk it out, I probably would've taken a lot longer to get that on my own
I think that is the best way of learning to :)
thanks for your help, i understand it better, not completely yet but making progress
No problem, take care!

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