Danielle Z.

asked • 05/26/14

What is the inverse of f(x)=15X^2? Determine if the inverse is a function.

I am trying to help a student understand functions and the inverse of functions.  Detailed steps on how to solve such a problem would be greatly appreciated.

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Francisco E. answered • 05/26/14

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Francisco; Civil Engineering, Math., Science, Spanish, Computers.

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f(x)=15X^2;
f(-1x)=15Y^2;
This takes us to x=15Y^2 and 
Y = √(x/15); I see it as a function.
 
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Kevin C.

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I think there is a slight problem with the domain.  Remember that the if you take the square root of y2, you have two answers, both the positive and the negative part.
 
i.e.  if y2 = x/15, then √(y2) = |y| = √(x/15),  and therefore y = +√(x/15), and y = -√(x/15).
 
This then is not a function.  However, if we redefine the domain of f(x) as x>=0, then the inverse is a function.  Is this correct?
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05/26/14

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