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anonymous

  • 5 years ago

How do you get this?:) let f(x)=(x+2)/(x+8) f^-1(-9)=?

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  1. amistre64
    • 5 years ago
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    you want the inverse of f(x)

  2. anonymous
    • 5 years ago
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    \[f^(-1)(x) = -(2 (4 x-1))/(x-1)\]

  3. amistre64
    • 5 years ago
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    the inverse is gotten suslly by switching x and y and resolves for y

  4. anonymous
    • 5 years ago
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    You don't have to find the inverse, Just plug f(x)=-9, and then solve for x. That value of x is the inverse at x=-9.

  5. anonymous
    • 5 years ago
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    let y = x+2 / x+8 yx + 8y = x+2 x(1-y) = 8y-2 x = (8y-2)/1-y which gives u d inverse now switch x and y and put in d value of x to get y

  6. anonymous
    • 5 years ago
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    thank you!:)

  7. amistre64
    • 5 years ago
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    x=(y+2)/(y+8) x(y+8)=y+2 xy +8x = y+2 xy - y = -8x +2 y(x-1) = -8x+2 y = (-8x+2) ------- (x-1)

  8. amistre64
    • 5 years ago
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    y = (-8(-9)+2)/(-9-1) y = 74/-10 = -7.4

  9. anonymous
    • 5 years ago
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    welll i did the very same

  10. amistre64
    • 5 years ago
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    yay!! its verified then ;)

  11. anonymous
    • 5 years ago
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    A simpler method, is to plug f(x)=-9 and then solve for x: \[-9={x+2 \over x+8} \implies -9x-72=x+2 \implies 10x=-74 \implies x=- 7.4\] So,\[f^{-1}(-9)=-7.4\]

  12. anonymous
    • 5 years ago
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    I like my method :P

  13. amistre64
    • 5 years ago
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    your method is just the same method rehashed lol

  14. anonymous
    • 5 years ago
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    Haha, not really.

  15. anonymous
    • 5 years ago
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    admit it, mine is better :P

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