anonymous
  • anonymous
What is the inverse function of f(x)=x^2 -10x+27, x>5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
It's a quadratic equation, someone find the roots, quick!
anonymous
  • anonymous
f(x) is just y so when finding the inverse you just have to switch out the x and y, like this:\[f(x)=x^2 -10x+27\]\[y=x^2 -10x+27\]\[\color{red}{x}=\color{red}{y}^2 -10\color{red}{y}+27\]now you have to solve for y, and that would be the inverse function, \(f^{-1}(x)\)
anonymous
  • anonymous
\[x=y^2−10y+27\]\[x-27=y^2-10y\]\[x-27+25=y^2-10y+25\]\[x-2=(y-5)^2\]\[\sqrt{x-2}=y-5\]\[\sqrt{x-2}+5=y\]\[y=\sqrt{x-2}+5\] \[f^{-1}(x)=\sqrt{x-2}+5\]

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anonymous
  • anonymous
I hope that helps! :)
anonymous
  • anonymous
Still need to find the restriction on the \(x\) for the inverse.
anonymous
  • anonymous
oh right... well since x is under the radical, we know \(x\ge2\)
anonymous
  • anonymous
and @Jazzyone2 isn't even here, lol
anonymous
  • anonymous
Yeah, looks like \(x>2\), and fortunately we can ignore the negative case on the radical because that would give values less than \(5\).
anonymous
  • anonymous
Sorry my ipad die so your saying the answer would be square root of x minus 2 plus five
anonymous
  • anonymous
No problem :) yes the answer is \(f^{-1}(x)=\sqrt{x-2}+5\)
anonymous
  • anonymous
Do I need to have the X>2 also? and thanks so much
anonymous
  • anonymous
its \(x\ge2\) and yea i guess, i mean if it asks :)
anonymous
  • anonymous
Okay Thanks you are a lifesaver!!!

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