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Functions Exam Question watch

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    f(x)=2x^2+4x+2 where XER and x>or equal to -1

    (a) Express f(x) in the form a(x+b)^2+c is 2(x+1)^2+2 correct?!

    (b) Describe fully two transformations which would map the graph of y=x^2, x>or equal to 0 onto the graph of y=f(x) (as stated above)

    (c) Find an expression for the inverse of f(x)



    Any help appreciated. Cheers !
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    for a)

    f(x)=2x^2 + 4x + 2
    =2(x^2 +2x) +2
    =2(x^2 + 2x + 1 ) +2 -2 (since adding 2 in the brackets leads to removing two here)
    =2(x+1)^2 (so c=0)
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    b) 1: Move the graph to the left parallel to the x-axis by 1 unit
    2: Stretch parallel to the y axis by factor 2
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    Hello!

    You translate y=x^2 left one unit, then stretch scale factor 2 parallel to the y-axis to get y=f(x).

    Inverse function:
    y=2(x+1)^2 Rearrange this to make x the subject of the formula.
    y/2 = (x+1)^2
    root(y/2) = x+1
    -1 + root(y/2) = x

    so inverse isf^-1(x)= -1 + root(x/2)

    love danniella
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    Excellent. :gthumb: Each of us conquered one part of the question.

    (Was too tired to do the 3rd part earlier, heh )
 
 
 
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Updated: April 7, 2006

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