Domain of a composite function without having g(x) function












1












$begingroup$


Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
$f(3x^2)$ $f(1-x)$ and $f(sin x)$

I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?



sorry for my bad English






functions function-and-relation-composition







share|cite|improve this question









$endgroup$

















    1












    $begingroup$


    Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
    $f(3x^2)$ $f(1-x)$ and $f(sin x)$

    I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
    When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?



    sorry for my bad English






    functions function-and-relation-composition







    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
      $f(3x^2)$ $f(1-x)$ and $f(sin x)$

      I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
      When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?



      sorry for my bad English






      functions function-and-relation-composition







      share|cite|improve this question









      $endgroup$




      Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
      $f(3x^2)$ $f(1-x)$ and $f(sin x)$

      I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
      When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?



      sorry for my bad English






      functions function-and-relation-composition




      functions function-and-relation-composition






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Dec 24 '18 at 6:47









      bashir sabooribashir saboori

      61




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          1 Answer
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          1












          $begingroup$

          Guide:



          We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$



          respetively since the output of $g$ needs to be a subset of domain of $f$.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            The range of $3x^2∈[0,1]$?
            $endgroup$
            – bashir saboori
            Dec 24 '18 at 7:11










          • $begingroup$
            You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:19












          • $begingroup$
            It's possible for $x$ to be negative.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:55











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          1 Answer
          1






          active

          oldest

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          active

          oldest

          votes






          active

          oldest

          votes









          1












          $begingroup$

          Guide:



          We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$



          respetively since the output of $g$ needs to be a subset of domain of $f$.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            The range of $3x^2∈[0,1]$?
            $endgroup$
            – bashir saboori
            Dec 24 '18 at 7:11










          • $begingroup$
            You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:19












          • $begingroup$
            It's possible for $x$ to be negative.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:55
















          1












          $begingroup$

          Guide:



          We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$



          respetively since the output of $g$ needs to be a subset of domain of $f$.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            The range of $3x^2∈[0,1]$?
            $endgroup$
            – bashir saboori
            Dec 24 '18 at 7:11










          • $begingroup$
            You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:19












          • $begingroup$
            It's possible for $x$ to be negative.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:55














          1












          1








          1





          $begingroup$

          Guide:



          We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$



          respetively since the output of $g$ needs to be a subset of domain of $f$.






          share|cite|improve this answer











          $endgroup$



          Guide:



          We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$



          respetively since the output of $g$ needs to be a subset of domain of $f$.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Dec 24 '18 at 7:54

























          answered Dec 24 '18 at 6:51









          Siong Thye GohSiong Thye Goh

          102k1468119




          102k1468119












          • $begingroup$
            The range of $3x^2∈[0,1]$?
            $endgroup$
            – bashir saboori
            Dec 24 '18 at 7:11










          • $begingroup$
            You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:19












          • $begingroup$
            It's possible for $x$ to be negative.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:55


















          • $begingroup$
            The range of $3x^2∈[0,1]$?
            $endgroup$
            – bashir saboori
            Dec 24 '18 at 7:11










          • $begingroup$
            You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:19












          • $begingroup$
            It's possible for $x$ to be negative.
            $endgroup$
            – Siong Thye Goh
            Dec 24 '18 at 7:55
















          $begingroup$
          The range of $3x^2∈[0,1]$?
          $endgroup$
          – bashir saboori
          Dec 24 '18 at 7:11




          $begingroup$
          The range of $3x^2∈[0,1]$?
          $endgroup$
          – bashir saboori
          Dec 24 '18 at 7:11












          $begingroup$
          You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
          $endgroup$
          – Siong Thye Goh
          Dec 24 '18 at 7:19






          $begingroup$
          You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
          $endgroup$
          – Siong Thye Goh
          Dec 24 '18 at 7:19














          $begingroup$
          It's possible for $x$ to be negative.
          $endgroup$
          – Siong Thye Goh
          Dec 24 '18 at 7:55




          $begingroup$
          It's possible for $x$ to be negative.
          $endgroup$
          – Siong Thye Goh
          Dec 24 '18 at 7:55


















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