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C3 inverse functions!?

just wanted to check my answer to a question-
if g(x)=(x+1)^2 +2 for x>0 is my original function, would the inverse be =
+/- √x-2 -1?
then i thought can't be a function as it is not a one-one function, so as the domain was x>0 i thought it would be a positive square root..but then when i sketch it, that won't be a reflection in the y=x axis as it should be. :confused:
and i'm also getting myself muddled with the domains and ranges of each. would the domain for original/range for inverse be x>0 and the range of original/domain of inverse be x>-2?
the more i look at it the more i'm confusing myself :tongue:
thankyou!
Original post by georgiaaaxo
just wanted to check my answer to a question-
if g(x)=(x+1)^2 +2 for x>0 is my original function, would the inverse be =
+/- √x-2 -1?
then i thought can't be a function as it is not a one-one function, so as the domain was x>0 i thought it would be a positive square root..but then when i sketch it, that won't be a reflection in the y=x axis as it should be. :confused:
and i'm also getting myself muddled with the domains and ranges of each. would the domain for original/range for inverse be x>0 and the range of original/domain of inverse be x>-2?
the more i look at it the more i'm confusing myself :tongue:
thankyou!


The positive square root is correct. However the domain for your inverse should be x>3. You will then see the reflection in the line y=x.
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Avatar for sputum
sputum
9
for the question as stated x>0 is the domain
so if x>0 what is (x+1)2 +2 greater than?
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georgiaaaxo
OP
8
Original post by Lord of the Flies
The positive square root is correct. However the domain for your inverse should be x>3. You will then see the reflection in the line y=x.


ohhh! of course. not sure where i got -2 from. thankyou!
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Avatar for georgiaaaxo
georgiaaaxo
OP
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Original post by sputum
for the question as stated x>0 is the domain
so if x>0 what is (x+1)2 +2 greater than?


x is greater than 3! thankyou :smile:


when i draw the graph, do i only draw the one positive line? i'm still a little confused as to how it is a reflection. the first one is a 'smiley face' quadratic right?
so how can the inverse be a reflection if you're only sketching the positives?
sorry for the questions, i missed the lesson on this topic :tongue:
Original post by georgiaaaxo
x is greater than 3! thankyou :smile:


when i draw the graph, do i only draw the one positive line? i'm still a little confused as to how it is a reflection. the first one is a 'smiley face' quadratic right?
so how can the inverse be a reflection if you're only sketching the positives?
sorry for the questions, i missed the lesson on this topic :tongue:


It would be a U-shaped parabola (i.e. a smiley face!) if the domain was R. Since you have x>0, it will only be part of the right hand side of that smiley face! Make sense?
Reply 6
Avatar for georgiaaaxo
georgiaaaxo
OP
8
Original post by Lord of the Flies
It would be a U-shaped parabola (i.e. a smiley face!) if the domain was R. Since you have x>0, it will only be part of the right hand side of that smiley face! Make sense?


ohhhhhhhhhhhh! yeah that makes sense. can't believe i didn't notice that aha :tongue:
clearly its been a long day! thankyou so much :biggrin:
got it!

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