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Math Help - Functions

  1. #1
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    Functions

    1) Simplify function
    g(g−1(2x−3))

    2)
    State the intervals on which the following function is negative: function

    f(x)= (1-x)^3(1+x)
    x^6(-1-2x)

    Express your answers using interval notation. For an interval (ab) , simply write (a,b). For in interval (−b) or (a)
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  2. #2
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    The first is a definition check.

    By Definition, the answer is '2x-3'. There are no calculations required. You tell me why.
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by lemontea View Post
    1) Simplify function
    g(g−1(2x−3))
    What's the matter with this question ?

    2)
    State the intervals on which the following function is negative: function

    f(x)= (1-x)^3(1+x)
    x^6(-1-2x)
    f(x)=\frac{(1-x)^3(1+x)}{x^6(-1-2x)}

    You should first study the sign of x\mapsto(1-x)^3, of x\mapsto1+x, of x\mapsto x, and of x\mapsto-1-2x then you'll be able to conclude using the rules concerning the quotient and the product of real numbers.
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  4. #4
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    i still dont get the second question ><''
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  5. #5
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by lemontea View Post
    i still dont get the second question ><''
    If you were asked to find where is x\mapsto (x-2)(x-3) negative, you could do this :

    x-3<0 \Leftrightarrow x<3 and x-2<0 \Leftrightarrow x<2

    Hence
    • if x<2 then \,x-3<0 and x-2<0 hence (x-3)(x-2)>0
    • if 2<x<3 then \,x-3<0 and x-2>0 hence (x-3)(x-2)<0
    • if x>3 then \,x-3>0 and x-2>0 hence (x-3)(x-2)>0
    We can conclude that (x-3)(x-2)<0\Leftrightarrow x\in]2,\,3[.

    Is it clearer ?
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  6. #6
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    i got the answers (-inf,-1) and (-1/2,1)...but it's incorrect..does anyone know why?
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  7. #7
    MHF Contributor Reckoner's Avatar
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    Question

    Quote Originally Posted by lemontea View Post
    i got the answers (-inf,-1) and (-1/2,1)...but it's incorrect..does anyone know why?
    Who says that they are incorrect? Those are the intervals that I find.
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