Question

What is the inverse function of f(x)=x^2 -10x+27, x>5

Answer 1

It's a quadratic equation, someone find the roots, quick!

Answer 2

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, \(f^{-1}(x)\)

Answer 3

\[x=y^2−10y+27\]\[x-27=y^2-10y\]\[x-27+25=y^2-10y+25\]\[x-2=(y-5)^2\]\[\sqrt{x-2}=y-5\]\[\sqrt{x-2}+5=y\]\[y=\sqrt{x-2}+5\]
\[f^{-1}(x)=\sqrt{x-2}+5\]

Answer 4

I hope that helps! :)

Answer 5

Still need to find the restriction on the \(x\) for the inverse.

Answer 6

oh right...
well since x is under the radical, we know \(x\ge2\)

Answer 7

and @Jazzyone2 isn't even here, lol

Answer 8

Yeah, looks like \(x>2\), and fortunately we can ignore the negative case on the radical because that would give values less than \(5\).

Answer 9

Sorry my ipad die so your saying the answer would be square root of x minus 2 plus five

Answer 10

No problem :) yes the answer is \(f^{-1}(x)=\sqrt{x-2}+5\)

Answer 11

Do I need to have the X>2 also? and thanks so much

Answer 12

its \(x\ge2\) and yea i guess, i mean if it asks :)

Answer 13

Okay Thanks you are a lifesaver!!!