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Let

f(x) = k(x) if x >= 1

f(x) = 2- x if x < 1

 

Find the function k(x) such that f(x) is its own inverse function.

 Aug 3, 2022
 #1
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For x<1, we have that f(x) = 2 - x.

We calculate the inverse by first setting f(x) = y, then solve for x

y = 2 - x, -x = y-2, x = 2 - y

so k(x) = 2 - x, and f(x) = 2 -x in the whole of R

The drawing from GeoGebra online shows that the mirror image og f(x) axross the line y = x is it's inverse function, k(x), which in this case has the same definition as f.

 Aug 3, 2022
edited by tuffla2022  Aug 3, 2022

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