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Mathematics 49 Online
OpenStudy (anonymous):

f(x)=-16x^2 What is the inverse function of.. I need the answer plzzzzzz, assume that all variables are positive. Again, does anyone know the answer? Someone out there is smart, i know there is.......

OpenStudy (amistre64):

x = -(16y^2) x/16 = -(y^2) sqrt(x)/4 = -y - sqrt(x)/4 = y

OpenStudy (amistre64):

maybe

OpenStudy (anonymous):

but that would come out to having an i in the final answer correct?

OpenStudy (amistre64):

nah, i made sure that I took out the -1 first to avoid that ...maybe lol let me look at it after drawing it

OpenStudy (anonymous):

amistre?

OpenStudy (amistre64):

yes?

OpenStudy (anonymous):

maybe i am tired but i think you missed this one.

OpenStudy (amistre64):

oh i miss alot of them ; not just this one lol

OpenStudy (anonymous):

ya, this thing is like impossible, it's a question on my test, what should i write down as the answer?

OpenStudy (amistre64):

its x = -y^2 but i dont think we can make a function out of it can we?

OpenStudy (anonymous):

f says square, then multiply by 16. f inverse says divide by -16, take the square root. should be \[f^{-1}(x)=\sqrt{-\frac{x}{16}}\]

OpenStudy (amistre64):

we can stick an absolute value in there cant we :)

OpenStudy (anonymous):

one to one because they restricted \[x>0\]

OpenStudy (amistre64):

\[y = \frac{\sqrt{|-x|}}{4}\]

OpenStudy (anonymous):

so function is defined only on positive x, and therefore is one to one. range is obviously negative numbers.

OpenStudy (anonymous):

i got f^-1=1/4(x) but i know that's wrong......

OpenStudy (anonymous):

no range is negative so domain of inverse is negative numbers

OpenStudy (amistre64):

\[\frac{\sqrt{|x|}}{4} ; D:(-\infty,0]\]

OpenStudy (amistre64):

maybe? lol

OpenStudy (anonymous):

i dont have to graph it

OpenStudy (anonymous):

absolute value not necessary just put \[\sqrt{\frac{-x}{4}}\]

OpenStudy (amistre64):

http://www.wolframalpha.com/input/?i=sqrt%28 |x|%29%2F4

OpenStudy (anonymous):

ah but that is not the inverse of this function.

OpenStudy (amistre64):

gotta run...ciao :)

OpenStudy (anonymous):

this function was restricted to positive x.

OpenStudy (anonymous):

ok later.

OpenStudy (amistre64):

it is if we rectric the domain lol; like trig inverse functions

OpenStudy (anonymous):

more puzzles please.

OpenStudy (anonymous):

123456789 are you confused yet?

OpenStudy (anonymous):

very......i'm a high school freshman in algebra 2 honors.... this is like crazy college crap lol

OpenStudy (anonymous):

let me try to xplain. do you know what the graph of \[y=-x^2\] looks like?

OpenStudy (anonymous):

yeah, it's a prarabola pointing down

OpenStudy (anonymous):

but we arent doing parabloas

OpenStudy (anonymous):

well the point is that since it is a parabola it is not a one to one function so it doesn't have an inverse. but they made it a one to one function by restricting the domain to positive numbers. so your actual graph is not a parabola, it is just the right hand side of the parabola. hterefore it is one to one

OpenStudy (anonymous):

so the way you do this is write \[y=-16x^2\] replace y by x and x by y to get \[x=-16y^2\]

OpenStudy (anonymous):

ok, now what?

OpenStudy (anonymous):

then solve for y: \[x=-16y^x\] \[\frac{-x}{16}=y^2\] \[y=\frac{\sqrt{-x}}{16}\]

OpenStudy (anonymous):

again the typesetting is bad. the square root should be over the whole thing.

OpenStudy (anonymous):

so it should be \[f^{-1}(x)=\frac{\sqrt{-x}}{4}\] since the square root of 16 is 4

OpenStudy (anonymous):

and you don't have to worry about \[\sqrt{-x}\] being a problem because the range of your original function was negative numbers, so your domain of the inverse is negative numbers.

OpenStudy (anonymous):

take out the i or leave it in?

OpenStudy (anonymous):

x is negative so -x is positive so you can take its square root.

OpenStudy (anonymous):

thanks a bunch

OpenStudy (anonymous):

leave it in. the domain of your original function was positive numbers so the range of your inverse must be positive numbers. do not put the minus sign outside. that would make the answer negative.

OpenStudy (anonymous):

welcome.

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