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abbie1

  • 3 years ago

Help!! Let f(x)=7x-13. Find f^-1(x). Let f(x)=x^2-16. Find f^-1(x).

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  1. saifoo.khan
    • 3 years ago
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    Do you know how to find an inverse?

  2. abbie1
    • 3 years ago
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    Okay thanks..

  3. hartnn
    • 3 years ago
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    ask if you still need help.

  4. abbie1
    • 3 years ago
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    I'm still confused..what am I finding the inverse to in my problem?? @hartnn

  5. hartnn
    • 3 years ago
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    ok, let y=7x-13 now to find the inverse, isolate x =... ? then just replace 'x' and 'y' (you can replace before isolating also.)

  6. abbie1
    • 3 years ago
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    -7x=-13-y?? why would there be a y in there??

  7. abbie1
    • 3 years ago
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    and then divide the whole thing by -7, but they're going to be fractions.

  8. hartnn
    • 3 years ago
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    y= 7x-13 add 13 to both sides, then divide by 7 [Let there be fractions, its ok]

  9. abbie1
    • 3 years ago
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    So basically you set the problem equal to 7x-13, and either make it equal to y or x?? There is no y in the problem? that's why i am confused

  10. abbie1
    • 3 years ago
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    x=-13-y/-7, and then do you want me to solve for x on y=7x-13 or that's what y equals?? So you use x to solve for y and y to solve for x??

  11. ohimai
    • 3 years ago
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    y = f(x).. They are the same thing

  12. abbie1
    • 3 years ago
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    x and y are the same thing??????

  13. hartnn
    • 3 years ago
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    i considered f(x) = y for simplicity. i'll write out steps so that you can understand. y= 7x-13 y+13 = 7x x = (y+13)/7 now to find inverse function just replace x and y y= (x+13)/7 so your inverse function is \[f^{-1}(x)=\dfrac{x+13}{7}\] got this ?

  14. ohimai
    • 3 years ago
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    f(x) and y are the same thing, so you re-write it as y = 7x-13

  15. ohimai
    • 3 years ago
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    got that part?

  16. abbie1
    • 3 years ago
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    Yes THANK YOU!!!!

  17. ohimai
    • 3 years ago
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    swop d x for d y.... it becomes x = 7y-13

  18. hartnn
    • 3 years ago
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    can you do same thing for f(x)=x^2-16. ?

  19. ohimai
    • 3 years ago
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    yep

  20. ohimai
    • 3 years ago
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    after swopping, solve for y

  21. ohimai
    • 3 years ago
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    7y= x+13 y = (x+13)/7

  22. abbie1
    • 3 years ago
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    Yes x=4 + sqrt y

  23. ohimai
    • 3 years ago
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    yes, but u have to swop d x and d y back... final answer would be y = 4 + sqrt(x)

  24. hartnn
    • 3 years ago
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    did u simplify like this ? \[\sqrt{16+y}=4+\sqrt y \] no, thats incorrect.

  25. abbie1
    • 3 years ago
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    by d do you mean the?

  26. ohimai
    • 3 years ago
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    yep

  27. abbie1
    • 3 years ago
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    sqrt. y+16=x^2 (Root over y+16)

  28. hartnn
    • 3 years ago
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    yeah, the inverse function will be \[f^{-1}(x)=\sqrt{x+16}\] no further simplification possible.

  29. hartnn
    • 3 years ago
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    ok ? got it ?

  30. abbie1
    • 3 years ago
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    Oh got it!!!

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