haleyelizabeth2017
  • haleyelizabeth2017
Find the inverse of f(x). (there are two)
Mathematics
katieb
  • katieb
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haleyelizabeth2017
  • haleyelizabeth2017
\[f(x)=-4x^2+1\]
haleyelizabeth2017
  • haleyelizabeth2017
Don't I switch f(x) and x to begin with?
Nnesha
  • Nnesha
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

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whpalmer4
  • whpalmer4
and solve for \(y\)
Nnesha
  • Nnesha
yes right
jdoe0001
  • jdoe0001
\(\bf f(x)={\color{blue}{ y}}=-4{\color{brown}{ x}}^2+1\qquad inverse\implies {\color{brown}{ x}}=-4{\color{blue}{ y}}^2+1\impliedby f^{-1}(x)\) yes
haleyelizabeth2017
  • haleyelizabeth2017
I got: \[y=\sqrt{\frac {x-1}{-4}}\]
Nnesha
  • Nnesha
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 \[\sqrt{x^2} = \pm x\]
haleyelizabeth2017
  • haleyelizabeth2017
wait, what? Sorry, you lost me there lol
Nnesha
  • Nnesha
\[\frac{ x }{ -4 }-\frac{ 1 }{ -4 } = -\frac{ x }{ 4 }+\frac{ 1 }{ 4 }\] -1 divided by -4 = positive 1/4
haleyelizabeth2017
  • haleyelizabeth2017
oh
Nnesha
  • Nnesha
|dw:1443653401397:dw|
Nnesha
  • Nnesha
hint \[\sqrt{\frac{ a }{ b }}=\frac{ \sqrt{a} }{ \sqrt{b} }\]
haleyelizabeth2017
  • haleyelizabeth2017
So, \[\frac{\sqrt{-x+1}}{2}\]?
Nnesha
  • Nnesha
looks good
haleyelizabeth2017
  • haleyelizabeth2017
Thank you :)
haleyelizabeth2017
  • haleyelizabeth2017
Is that all?
Nnesha
  • Nnesha
yes that's it
haleyelizabeth2017
  • haleyelizabeth2017
Awesome! :) And it is also a function, correct?

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