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Let 

f(x)  = k(x) if x > 3

f(x) = (x - 3)^2 + 3 if x <= 3

 

Find k(x) such that f is it's own inverse.

 Feb 7, 2021
 #1
avatar+118696 
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Let 

f(x)  = k(x) if x > 3

f(x) = (x - 3)^2 + 3 if x <= 3                                 x<=3,  y>3

 

Find k(x) such that f is it's own inverse.

 

y=(x - 3)^2 + 3

make x the subject

x=±y3+3For the inverse, swap x and yy=±x3+3buty3andx>3 Since y is negative it must be the - signy=x3+3wherex>3

 

so 

k(x)=x3+3wherex>3

 

 Feb 7, 2021

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