anonymous
  • anonymous
if f(x)=-6x+6, then f^-1(x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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UsukiDoll
  • UsukiDoll
any attempts?
anonymous
  • anonymous
solve \[x=-6y+6\] for \(y\) in two steps
UsukiDoll
  • UsukiDoll
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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More answers

anonymous
  • anonymous
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
anonymous
  • anonymous
but solving \[x=-6y+6\] for \(y\) takes two steps, so it is just as quick as thinking
anonymous
  • anonymous
I'm confused
anonymous
  • anonymous
can you work through it with me?
anonymous
  • anonymous
please? all my attempts arent working out
anonymous
  • anonymous
@UsukiDoll
anonymous
  • anonymous
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)
anonymous
  • anonymous
I know the steps but I usually get stuck when solving for y
anonymous
  • anonymous
\[y=-6x+6 \] \[x=-6y+6\] what would your first step be to solving for y?
anonymous
  • anonymous
Try your best, don't be afraid to make mistakes
anonymous
  • anonymous
get rid of + 6 by subtracting six from both sides
anonymous
  • anonymous
There you go, good job, so we have \[x-6 = -6y\] now what?
anonymous
  • anonymous
divide by negative 6
anonymous
  • anonymous
Good! \[y = \frac{ -(x-6) }{ 6 }\] you may simplify that now
anonymous
  • anonymous
how?
anonymous
  • anonymous
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?
anonymous
  • anonymous
What should we replace y with :)
anonymous
  • anonymous
the rule for negative functions
anonymous
  • anonymous
|dw:1436932582839:dw|
anonymous
  • anonymous
\[f^{-1}(x) = \frac{ 6-x }{ 6 }\] yup :)
anonymous
  • anonymous
Not so bad right? Just have to try it and you'll start getting it!
anonymous
  • anonymous
it helps to talk it out, I probably would've taken a lot longer to get that on my own
anonymous
  • anonymous
I think that is the best way of learning to :)
anonymous
  • anonymous
thanks for your help, i understand it better, not completely yet but making progress
anonymous
  • anonymous
No problem, take care!

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