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I have $f(x) = \sqrt x$, which means $f^{-1}(x) = x^2$.

I need to determine if the points $(a, f(a))$ where $a \geq 0$ lies on the graph of $f$ or $f^{-1}$. This was easier with points like $(2,4)$ or $(5, \sqrt 5)$ where I could easily plug in the numbers and solve the equation. Does the same hold where I just use the terms $a$ and $f(a)$ to solve the problem?

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A similar example would the point (f(a),a). –  erimar77 Oct 25 '11 at 22:03
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Hint: do you have a definition of what "the graph of $f$" means, that you could compare to? –  Henning Makholm Oct 25 '11 at 22:08
    
I would assume the graph f(x)= sqrt x –  erimar77 Oct 25 '11 at 22:12
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He is asking if you have the definition for "the graph of a function," in general. If you do, the answer can be drawn from that. –  AMPerrine Oct 25 '11 at 22:18
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Taken from Wikipedia: "In mathematics, the graph of a function $f$ is the collection of all ordered pairs $(x, f(x))$." So clearly the general form is correct in your example. If $a$ is in the domain then you can be sure the point is on the graph. –  AMPerrine Oct 25 '11 at 22:30
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up vote 1 down vote accepted

I suppose this comment evolved to the point of being an answer, so I will make it one:

Taken from Wikipedia: "In mathematics, the graph of a function $f$ is the collection of all ordered pairs $(x,f(x))$." So clearly the general form is correct in your example. If $a$ is in the domain then you can be sure the point is on the graph of $f$.

$(f(a),a)$ would not be on the graph of $f$ except for some specific $a$.

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