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anonymous

  • one year ago

if f(x)=-5x-13 than f^-1(x)=?

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  1. freckles
    • one year ago
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    the first step is to solve y=-5x-13 for x.

  2. freckles
    • one year ago
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    For example, I bet you know how to solve 5=-5x-13 for x. You would add 13 on both sides right? 5+13=-5x then divide both sides by -5 (5+13)/(-5)=x just do the same thing here but instead of 5 you have y

  3. anonymous
    • one year ago
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    I would add 13 to both sides and divide both sides by -5 which i guess would leave me with 5=x

  4. anonymous
    • one year ago
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    I don't understand how to do the same with y though

  5. jim_thompson5910
    • one year ago
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    |dw:1436928354040:dw|

  6. jim_thompson5910
    • one year ago
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    first add 13 to both sides |dw:1436928386487:dw|

  7. jim_thompson5910
    • one year ago
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    that is done to cancel out the '-13' on the right side |dw:1436928424337:dw| since -13 and +13 add to 0. The 0 goes away

  8. jim_thompson5910
    • one year ago
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    after adding 13 to both sides, we now have y+13 = -5x with me so far?

  9. anonymous
    • one year ago
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    so far yes

  10. jim_thompson5910
    • one year ago
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    |dw:1436928497040:dw|

  11. jim_thompson5910
    • one year ago
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    the next step is to undo the "-5 times x" so we divide both sides by -5 which will isolate x |dw:1436928547068:dw|

  12. jim_thompson5910
    • one year ago
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    -5 divided by itself gives 1 1 times x = x, so the '1' goes away leaving just x behind |dw:1436928578962:dw|

  13. jim_thompson5910
    • one year ago
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    once we get \[\Large x = \frac{y+13}{-5}\] we swap x and y to get \[\Large y = \frac{x+13}{-5}\] and this is the inverse. We can write that inverse as \[\Large f^{-1}(x) = \frac{x+13}{-5}\]

  14. anonymous
    • one year ago
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    Thank you for your help

  15. jim_thompson5910
    • one year ago
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    you're welcome

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