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    sin^2 x \equiv (sin x)^2

    Why does

    sin^{-1} x \not= (sinx)^{-1}

    What do the inverse functions actually mean?

    The function notation is ambiguous. Writing brackets around  \sin x is annoying, Hence we put  \sin ^2 x to save time.

    However when we have "general notation" we get  f^{-1}(x) means the inverse function of x. However  f^{2}(x) = f(f(x)) , The notation is a big mess. For trig functions we normally use  \arcsin x


f(x) \equiv sin x \Rightarrow f^{-1}(x) \equiv \arcsin x
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Updated: October 24, 2015
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