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C3 inverse functions!?

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    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
    thankyou!
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    (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
    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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    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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    (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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    (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


    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
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    (Original post by georgiaaaxo)
    x is greater than 3! thankyou


    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
    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?
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    (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
    clearly its been a long day! thankyou so much
    got it!

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