Maths Function properties

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this may be quite a simple question but please can someone let me know if everything written on this image is correct? Thank you, any help is much appreciated. (https://i.stack.imgur.com/0Sozz.jpg)







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    this may be quite a simple question but please can someone let me know if everything written on this image is correct? Thank you, any help is much appreciated. (https://i.stack.imgur.com/0Sozz.jpg)







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      up vote
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      favorite









      up vote
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      this may be quite a simple question but please can someone let me know if everything written on this image is correct? Thank you, any help is much appreciated. (https://i.stack.imgur.com/0Sozz.jpg)







      share|cite|improve this question












      this may be quite a simple question but please can someone let me know if everything written on this image is correct? Thank you, any help is much appreciated. (https://i.stack.imgur.com/0Sozz.jpg)









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      asked Aug 26 at 22:49









      user564900

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          yes, the mathematics written on the paper is correct.



          Unfortunately the notation inverse function is very very confusing.



          Students get confused by for example the difference between $$ sin ^-1 x $$ and $$ frac 1sin x$$ where the first one is the inverse sine function and the second one is the co-secant function, which are totally different functions.



          After some practice it gets easier to find out which is which from the context.






          share|cite|improve this answer




















          • Thank you for your reply. Yes the false ‘arcsin(x) = cosec(x)’ statement is what led me to find out if ‘f^-1(x) is not equal to (f(x))^-1’ is true for all functions aswell as trig functions.
            – user564900
            Aug 27 at 0:27










          • @user564900 Thanks for your attention and understanding .
            – Mohammad Riazi-Kermani
            Aug 27 at 0:28










          Your Answer




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          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          2
          down vote













          yes, the mathematics written on the paper is correct.



          Unfortunately the notation inverse function is very very confusing.



          Students get confused by for example the difference between $$ sin ^-1 x $$ and $$ frac 1sin x$$ where the first one is the inverse sine function and the second one is the co-secant function, which are totally different functions.



          After some practice it gets easier to find out which is which from the context.






          share|cite|improve this answer




















          • Thank you for your reply. Yes the false ‘arcsin(x) = cosec(x)’ statement is what led me to find out if ‘f^-1(x) is not equal to (f(x))^-1’ is true for all functions aswell as trig functions.
            – user564900
            Aug 27 at 0:27










          • @user564900 Thanks for your attention and understanding .
            – Mohammad Riazi-Kermani
            Aug 27 at 0:28














          up vote
          2
          down vote













          yes, the mathematics written on the paper is correct.



          Unfortunately the notation inverse function is very very confusing.



          Students get confused by for example the difference between $$ sin ^-1 x $$ and $$ frac 1sin x$$ where the first one is the inverse sine function and the second one is the co-secant function, which are totally different functions.



          After some practice it gets easier to find out which is which from the context.






          share|cite|improve this answer




















          • Thank you for your reply. Yes the false ‘arcsin(x) = cosec(x)’ statement is what led me to find out if ‘f^-1(x) is not equal to (f(x))^-1’ is true for all functions aswell as trig functions.
            – user564900
            Aug 27 at 0:27










          • @user564900 Thanks for your attention and understanding .
            – Mohammad Riazi-Kermani
            Aug 27 at 0:28












          up vote
          2
          down vote










          up vote
          2
          down vote









          yes, the mathematics written on the paper is correct.



          Unfortunately the notation inverse function is very very confusing.



          Students get confused by for example the difference between $$ sin ^-1 x $$ and $$ frac 1sin x$$ where the first one is the inverse sine function and the second one is the co-secant function, which are totally different functions.



          After some practice it gets easier to find out which is which from the context.






          share|cite|improve this answer












          yes, the mathematics written on the paper is correct.



          Unfortunately the notation inverse function is very very confusing.



          Students get confused by for example the difference between $$ sin ^-1 x $$ and $$ frac 1sin x$$ where the first one is the inverse sine function and the second one is the co-secant function, which are totally different functions.



          After some practice it gets easier to find out which is which from the context.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 26 at 23:20









          Mohammad Riazi-Kermani

          30.6k41852




          30.6k41852











          • Thank you for your reply. Yes the false ‘arcsin(x) = cosec(x)’ statement is what led me to find out if ‘f^-1(x) is not equal to (f(x))^-1’ is true for all functions aswell as trig functions.
            – user564900
            Aug 27 at 0:27










          • @user564900 Thanks for your attention and understanding .
            – Mohammad Riazi-Kermani
            Aug 27 at 0:28
















          • Thank you for your reply. Yes the false ‘arcsin(x) = cosec(x)’ statement is what led me to find out if ‘f^-1(x) is not equal to (f(x))^-1’ is true for all functions aswell as trig functions.
            – user564900
            Aug 27 at 0:27










          • @user564900 Thanks for your attention and understanding .
            – Mohammad Riazi-Kermani
            Aug 27 at 0:28















          Thank you for your reply. Yes the false ‘arcsin(x) = cosec(x)’ statement is what led me to find out if ‘f^-1(x) is not equal to (f(x))^-1’ is true for all functions aswell as trig functions.
          – user564900
          Aug 27 at 0:27




          Thank you for your reply. Yes the false ‘arcsin(x) = cosec(x)’ statement is what led me to find out if ‘f^-1(x) is not equal to (f(x))^-1’ is true for all functions aswell as trig functions.
          – user564900
          Aug 27 at 0:27












          @user564900 Thanks for your attention and understanding .
          – Mohammad Riazi-Kermani
          Aug 27 at 0:28




          @user564900 Thanks for your attention and understanding .
          – Mohammad Riazi-Kermani
          Aug 27 at 0:28

















           

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