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haleyelizabeth2017

  • one year ago

Find the inverse of f(x). (there are two)

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  1. haleyelizabeth2017
    • one year ago
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    \[f(x)=-4x^2+1\]

  2. haleyelizabeth2017
    • one year ago
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    Don't I switch f(x) and x to begin with?

  3. Nnesha
    • one year ago
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    f(x) is same as y so we can rewrite this as \[\huge\rm y=-4x^2+1\] to find inverse switch x and y

  4. whpalmer4
    • one year ago
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    and solve for \(y\)

  5. Nnesha
    • one year ago
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    yes right

  6. jdoe0001
    • one year ago
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    \(\bf f(x)={\color{blue}{ y}}=-4{\color{brown}{ x}}^2+1\qquad inverse\implies {\color{brown}{ x}}=-4{\color{blue}{ y}}^2+1\impliedby f^{-1}(x)\) yes

  7. haleyelizabeth2017
    • one year ago
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    I got: \[y=\sqrt{\frac {x-1}{-4}}\]

  8. Nnesha
    • one year ago
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    hmm \[\huge\rm \color{ReD}{x}=-4\color{blue}{y}^2+1\] divide by -4 \[\frac{ x-1 }{ -4 } \] is same as \[\huge\rm \frac{ x }{ -4 } -\frac{ 1 }{ -4 }\] first divide the sign and then take square root and remember when we take square root we should get 2 solutions \[\sqrt{x^2} = \pm x\]

  9. haleyelizabeth2017
    • one year ago
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    wait, what? Sorry, you lost me there lol

  10. Nnesha
    • one year ago
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    \[\frac{ x }{ -4 }-\frac{ 1 }{ -4 } = -\frac{ x }{ 4 }+\frac{ 1 }{ 4 }\] -1 divided by -4 = positive 1/4

  11. haleyelizabeth2017
    • one year ago
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    oh

  12. Nnesha
    • one year ago
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    |dw:1443653401397:dw|

  13. Nnesha
    • one year ago
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    hint \[\sqrt{\frac{ a }{ b }}=\frac{ \sqrt{a} }{ \sqrt{b} }\]

  14. haleyelizabeth2017
    • one year ago
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    So, \[\frac{\sqrt{-x+1}}{2}\]?

  15. Nnesha
    • one year ago
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    looks good

  16. haleyelizabeth2017
    • one year ago
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    Thank you :)

  17. haleyelizabeth2017
    • one year ago
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    Is that all?

  18. Nnesha
    • one year ago
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    yes that's it

  19. haleyelizabeth2017
    • one year ago
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    Awesome! :) And it is also a function, correct?

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