anonymous
  • anonymous
How do I find the inverse of f(x) when the equation is: f(x)=(x+3)^2, x<-3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
The answer is supposed to be f-1(x)= -√x - 3, but why?
.Sam.
  • .Sam.
y=(x+3)^{2} \[x=\sqrt{y}-3\] \[f^{-1}x=\sqrt{x}-3\]
anonymous
  • anonymous
how is y square rooted instead of x? o.O

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apoorvk
  • apoorvk
inverse of a function is all about writing y in terms of x. |dw:1332717872871:dw| now interchange x and y to get get the inverse of y.( i dont think there would be a '-' before sqrt(y) in the answer you posted)
.Sam.
  • .Sam.
Let y=(x+3)^{2} Find x x=-√y−3 \[f^{−1}(x)=-√x−3\]
anonymous
  • anonymous
but i still don't get how
apoorvk
  • apoorvk
that is protocol for writing an inverse function.. because ultimately we need the function's mirror image about y=x |dw:1332718104866:dw| (just an example)
anonymous
  • anonymous
@milliex51 Do you understand it?
anonymous
  • anonymous
no D:
anonymous
  • anonymous
Simply put! Firstly, You need to know the technique of finding inverse function
anonymous
  • anonymous
y =(x+3)² First step is solve for x:
anonymous
  • anonymous
alright.
anonymous
  • anonymous
Taking square root both sides
anonymous
  • anonymous
alright so it'll be \[\sqrt{x} = \sqrt{y+3)^{2}}\]
anonymous
  • anonymous
Don't interchange x, y early,
anonymous
  • anonymous
oh so then how? D: and why not?
anonymous
  • anonymous
You'll be confused by multi steps at the same time!
anonymous
  • anonymous
ohh, okay.
anonymous
  • anonymous
√y = √ (x+3)² Now, what can you get next?
anonymous
  • anonymous
I can transpose +3 to y and turn it to y-3?
anonymous
  • anonymous
keep in mind, our purpose is solve for x FIRST
anonymous
  • anonymous
alright.
anonymous
  • anonymous
RIGHT, work on it!
anonymous
  • anonymous
so I interchange y to x?
anonymous
  • anonymous
√ (x+3)² = ???
anonymous
  • anonymous
y
anonymous
  • anonymous
You need to focus on X: ± ( x + 3)
anonymous
  • anonymous
ohhh ..
anonymous
  • anonymous
Then from the condition x < -3 => take the solution - ( x + 3)
anonymous
  • anonymous
Now plug it back to the expression:
anonymous
  • anonymous
√y = √ (x+3)² ???
anonymous
  • anonymous
which expression?
anonymous
  • anonymous
I mean the equation!
anonymous
  • anonymous
√y = -√(x+3)^2?
anonymous
  • anonymous
What's the purpose of taking square root?
anonymous
  • anonymous
to cancel the square?
anonymous
  • anonymous
show me how ?
anonymous
  • anonymous
that I don't know.
anonymous
  • anonymous
You just said CANCEL SQUARE!
anonymous
  • anonymous
why are you using block letters? Man, I don't appreciate your responses.
anonymous
  • anonymous
It's my habbit so the asker catch the main idea!
anonymous
  • anonymous
If you feel trouble, I don't force it :)

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