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anonymous

  • one year ago

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

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  1. UsukiDoll
    • one year ago
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    any attempts?

  2. anonymous
    • one year ago
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    solve \[x=-6y+6\] for \(y\) in two steps

  3. UsukiDoll
    • one year ago
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    that's what I was thinking.. swap the variables.. solve for y and then replace y with the f inverse notation .

  4. anonymous
    • one year ago
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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

  5. anonymous
    • one year ago
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    but solving \[x=-6y+6\] for \(y\) takes two steps, so it is just as quick as thinking

  6. anonymous
    • one year ago
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    I'm confused

  7. anonymous
    • one year ago
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    can you work through it with me?

  8. anonymous
    • one year ago
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    please? all my attempts arent working out

  9. anonymous
    • one year ago
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    @UsukiDoll

  10. anonymous
    • one year ago
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    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)

  11. anonymous
    • one year ago
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    I know the steps but I usually get stuck when solving for y

  12. anonymous
    • one year ago
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    \[y=-6x+6 \] \[x=-6y+6\] what would your first step be to solving for y?

  13. anonymous
    • one year ago
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    Try your best, don't be afraid to make mistakes

  14. anonymous
    • one year ago
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    get rid of + 6 by subtracting six from both sides

  15. anonymous
    • one year ago
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    There you go, good job, so we have \[x-6 = -6y\] now what?

  16. anonymous
    • one year ago
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    divide by negative 6

  17. anonymous
    • one year ago
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    Good! \[y = \frac{ -(x-6) }{ 6 }\] you may simplify that now

  18. anonymous
    • one year ago
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    how?

  19. anonymous
    • one year ago
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    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?

  20. anonymous
    • one year ago
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    What should we replace y with :)

  21. anonymous
    • one year ago
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    the rule for negative functions

  22. anonymous
    • one year ago
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    |dw:1436932582839:dw|

  23. anonymous
    • one year ago
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    \[f^{-1}(x) = \frac{ 6-x }{ 6 }\] yup :)

  24. anonymous
    • one year ago
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    Not so bad right? Just have to try it and you'll start getting it!

  25. anonymous
    • one year ago
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    it helps to talk it out, I probably would've taken a lot longer to get that on my own

  26. anonymous
    • one year ago
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    I think that is the best way of learning to :)

  27. anonymous
    • one year ago
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    thanks for your help, i understand it better, not completely yet but making progress

  28. anonymous
    • one year ago
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    No problem, take care!

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