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.
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=±√y−3+3For the inverse, swap x and yy=±√x−3+3buty≤3andx>3 Since y is negative it must be the - signy=−√x−3+3wherex>3
so
k(x)=−√x−3+3wherex>3