Question

Function help? How do I solve this?

Answer 1

well for the restricted domain is the right hand part of the parabola
[-3, oo)

Answer 2

let me show you the graph

Answer 3

http://prntscr.com/6rukzb

Answer 4

we will divide the graph to two and take the right part only [-3,oo)
so our function will be one-to-one correspandance

Answer 5

so know we are ready to find the inverse function

Answer 6

start with f(x)=-(x+3)^2-4

Answer 7

are you even there, or you are the kind that awaits for the result and not putting effort
I might be wrong, so prove me wrong and show me you are willing to solve this

Answer 8

@xapproachesinfinity I'm here, just not staring at my question for an hour waiting for help, hang on

Answer 9

Ok
put y=-(x+3)^2-4
\[\rm y=-(x+3)^2-4 \\ x=-(y+3)^2-4 ~~\longleftarrow ~switch~x~with~y~~~~ \]

Answer 10

then solve for y

Answer 11

\[\large \rm x+4=-(y+3)^2 \\ -(x+4)=(y+3)^2 \\ \sqrt{-(x+4)}=y+3~~here~x\ge-3 \]
\[-3+\sqrt{-x-4}=y \Longrightarrow f^{-1}(x)=-3+\sqrt{-x-4}\]

Answer 12

I meant y>= -3 in the line 3
no x
just to make things reasonable

Answer 13

@xapproachesinfinity sorry kind of lost me

Answer 14

are you having trouble with finding the inverse?