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Find the range of the function

  1. Aug 17, 2010 #1
    1. The problem statement, all variables and given/known data

    The function f is defined by

    f(x) = sqrt(7-3x) , x<=1

    = 3x^2-4x+3 , x>1

    (1) Find the range of f

    (2) if g(x)=sqrt(7-3x) , h(x)=3x^2-4x+3 in the case where f is continuous , find the composite function hg and state its domain and range.

    (3) Determine the largest set for the domain and the corresponding range such that hg is one to one.

    2. Relevant equations



    3. The attempt at a solution

    (1) Range=[2,infinity)

    (2) hg(x)=24-9x-4sqrt(7-3x)

    domain=(- inifinity , 7/3)

    range = [3 , infinity)

    (3) some hints on this.
     
  2. jcsd
  3. Aug 17, 2010 #2

    vela

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    Re: fucntions

    You didn't get the correct range in part (2).

    Try plotting hg(x). It'll help you see the answers for parts (2) and (3).
     
  4. Aug 18, 2010 #3
    Re: fucntions

    ok

    got it!Thanks again Vela!
     
    Last edited: Aug 18, 2010
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