Math Help - inverse function help

I dont know if this is right...

i need inverse function of g(x)= -2(x+3)^2 +8 (-5less than or equal to x less than or equal to -3)

so i got... x= -2(y+3)^2 +8
x-8=-2(y+3)^2
-1/2(x-8)= (y+3)^2
square root both sides gives g-1(x)= √ -1/2(x-8)-3
but this seems horribly wrong, - under a root and how do i find the domain from that??

First you have to prove that g is bijective, if you do that the problem is like solved.

"so i got... x= -2(y+3)^2 +8
x-8=-2(y+3)^2
-1/2(x-8)= (y+3)^2
square root both sides gives g-1(x)= √ -1/2(x-8)-3"

I don't understand - you should just calculate, then find (or do that when you prove that g is surjective) and the root that is in the interval you want it to be.

Originally Posted by dragon555

I dont know if this is right...

i need inverse function of g(x)= -2(x+3)^2 +8 (-5less than or equal to x less than or equal to -3)

so i got... x= -2(y+3)^2 +8
x-8=-2(y+3)^2
-1/2(x-8)= (y+3)^2
square root both sides gives g-1(x)= √ -1/2(x-8)-3
but this seems horribly wrong, - under a root and how do i find the domain from that??

, with domain

range of is

note that the range of is the domain of ...











for the domain , you want the range to be

Originally Posted by dragon555

I dont know if this is right...

i need inverse function of g(x)= -2(x+3)^2 +8 (-5less than or equal to x less than or equal to -3)

so i got... x= -2(y+3)^2 +8
x-8=-2(y+3)^2
-1/2(x-8)= (y+3)^2
square root both sides gives g-1(x)= √ -1/2(x-8)-3
but this seems horribly wrong, - under a root and how do i find the domain from that??

It seesm that this question might be part of an assignment that counts towards your final grade. See rule #6: http://www.mathhelpforum.com/math-he...hp?do=vsarules. Thread closed.