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F(x)=f(2x)=3. Is it strictly a constant function?

  1. Feb 12, 2012 #1
    f(x)=f(2x)=3. Is it strictly a constant function??

    1. The problem statement, all variables and given/known data

    f(x)=f(2x)=3.
    can we say that it is constant. Nothing else..

    2. Relevant equations

    BRAIN>>>>

    3. The attempt at a solution

    f(1)=f(1/2)=f(1/4)=f(1/8).........f(1/∞)=f(0)=3
    I think no there can be many functions having such property and constant function is one of them.
    AM i correct..?
     
  2. jcsd
  3. Feb 12, 2012 #2

    HallsofIvy

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    Re: f(x)=f(2x)=3. Is it strictly a constant function??

    If you are saying that f(x)= 3 for all x, yes, that is a constant function. There are NOT "many functions" such that f(x)= 3 for all x!
     
  4. Feb 14, 2012 #3
    Re: f(x)=f(2x)=3. Is it strictly a constant function??

    Is it possible for a function that it is not a constant function and obey the above written property?????
     
  5. Feb 14, 2012 #4
    Re: f(x)=f(2x)=3. Is it strictly a constant function??

    no, for example, take f(x) =(-6)*cos(x), and x = 2pi/3. What do you get?
     
  6. Feb 14, 2012 #5
    Re: f(x)=f(2x)=3. Is it strictly a constant function??

    oh, is it for all x? then, yes, provided that f is continuous around x=0.
     
  7. Feb 14, 2012 #6
    Re: f(x)=f(2x)=3. Is it strictly a constant function??

    lol, your problem is trivial:
    [tex]
    \left( \forall x \right) f(x) = f(2x) = 3 \Rightarrow \left( \forall x\right) f(x) = 3
    [/tex]
    This is by definition a constant function!
     
  8. Feb 14, 2012 #7
    Re: f(x)=f(2x)=3. Is it strictly a constant function??

    To start , Forget about f(2x) for a while... f(x) = 3 implies that irrespective of what values the variable 'x' can take, the function value is 3 only... so , f(x) = 3 is a constant function for all values of x...The set of values takne by '2x' is actually a subset of values taken by 'x'...
    This means that f(2x) is a subset of values taken by f(x).So , f(2x) is also a constant function like f(x).
    The answer is : yes , the function is strictly constant
     
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