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y^{-1}=\frac{9}{x^2} (Find the inverse of 9/x^2. thanks!

 Sep 20, 2015
 #1
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Your answer is=x^2/9

 Sep 20, 2015
 #2
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This function  has no inverse because it is not one- to-one

 

However......if we restrict the domain of the original function, we can get two separate inverses

 

y = 9x^2     divide both sides by 9

 

y/9 = x^2   take the pos/neg square roots of both sides

 

[pos/neg] sqrt( y/9)  = x   exchange x and y

 

[pos/neg] sqrt( x/9)  = y  = f-1(x)

 

If the domain of the original function is from (-inf, 0), then neg sqrt(x/9)  is the inverse

 

If the domain of the original function is from (0, inf), then pos sqrt(x /9)  is the inverse

 

[ BTW, the origin point (0, 0)  could belong to either inverse function ]

 

 

 

cool cool cool

 Sep 21, 2015

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