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avatar+397 

Let\(f(x) = \begin{cases} k(x) &\text{if }x>0, \\ -\frac1{2x}&\text{if }x< 0\\ 0&\text{if }x=0. \end{cases} \)Find the function k(x) such that f(x) is its own inverse function.

 Apr 14, 2020
 #1
avatar+21004 
+1

The equation   y = x   is its own inverse.

 Apr 14, 2020
 #2
avatar+397 
-1

Thats not an answer

qwertyzz  Apr 15, 2020
 #3
avatar+109524 
+1

the inverse of 

\(y=-\frac{1}{2x}\qquad where \qquad x<0\\is\\ x=-\frac{1}{2y} \qquad where \qquad x>0\\ rearrange\\ y=-\frac{1}{2x} \qquad where \qquad x>0\\ \)

 

so

\(k(x)=-\frac{1}{2x}\)

.
 Apr 15, 2020

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