How do I tell whether each relationship is inverse relation?

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
snoopy2722
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How do I tell whether each relationship is inverse relation?

Postby snoopy2722 » Tue Jun 02, 2009 6:24 am

How do I tell whether each relationship is an inverse relation?

x=y/5

xy=8

Thank you.

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stapel_eliz
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Postby stapel_eliz » Tue Jun 02, 2009 12:44 pm

snoopy2722 wrote:How do I tell whether each relationship is an inverse relation?

If you are asking how to show that two relations are inverses of each other, the usual process is to compose the two functions.

For instance, your two relations may be restated as functions, first by solving each for "y=":

. . . . .y = 5x

. . . . .y = 8/x

...and then renaming:

. . . . .f(x) = 5x

. . . . .g(x) = 8/x

Then compose the two functions:

. . . . .f(g(x)) or g(f(x))

...and see if you end up with just "x". If you do, the functions are inverses of each other. Otherwise, they aren't.

If you mean something else, kindly please reply with clarification. Thank you! :wink:


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